I used to bend over backwards "amending" my heavy clay soils, using cover crops, double-digging - the whole 9 yards. Until one year I dug into the ground and found the cover crop I had planted last year perfectly preserved between the layers of cold, gray clay where I had dug it in the year before. So I went with mulching - because a few years before that, I had a plot in a community garden where we had access to a gigantic pile of hay. I mulched to a depth of over 12" - AFTER the hay had settled - it was the middle of a drought that year and I had the best garden I had ever had, despite having to haul water to the site in milk jugs. Which, btw, were a fairly new innovation at the time, and cost more than buying the milk in cardboard cartons. Since then I have found that unless you live in slug central, a double layer of broken down brown corrugated cardboard boxes covered by the cheap or free mulch of your choice - even including bagged wood mulches, as long as you avoid the ones that are dyed - and a drip irrigation system leave you with as near to a carefree garden as one could possibly hope for and still be living in the real world. Oh yeah, and not having other people do all the work for you, LOL! Mulching and measured drip irrigation also, it turns out, encourages earthworms, and that IS just like having other people do all the work for you as far as soil amendments. They aerate, they pull down the lower layers of mulch into the soil as it decomposes, they do all that soil "mixing" that double digging was supposed to do at the expense of back breaking labor. Except worms don't HAVE a backbone and this is what they do naturally. Don't pull the cardboard up to the base of the plants, instead leave an area clear all the way around the stem for where you will put your emitters (or aim your watering wand if you hand water). I also habitually plant everything but row crops (like peas) in a bowl-shaped depression to funnel water to the plant roots. I leave more area free around tomatoes because I plant them trench-style - I pluck off all but the top one or two sets of leaves, dig a trench that slopes upwards to where I want the stem to emerge. This encourages root development along the entire stem. I leave that entire area free of the cardboard mulch so the entire stem can easily be watered. I do pull the top mulch, which is usually wood mulch now that I'm stuck in suburbia, across the trench, but not all the way up to the stem. Leaving that clear eliminates slug damage, though that's not usually been a problem for me. If you have access to something easily compostable like straw or hay, you can just keep layering it with new mulch every year. Yes, hay has the reputation for being weedy, but you won't much notice that if you keep the mulch deep. Also the cardboard layers help to keep any weeds from rooting well, and the thick mulch makes anything that manages to poke its head above the top very spindly and easy to pull. Still, you might want to avoid hay when possible because sometimes it can infest your garden with bindweed, the seeds of which can lie dormant in the soil for virtually ever. This is only a problem when you STOP mulching, but there it is. The year I had access to unlimited amounts of hay, there were already much worse things than bindweed in that field, which had been farmed for decades and was thoroughly infested with giant hogweed already. However in an urban setting I've found that bagged wood mulches work just fine and with the cardboard underlayment, you don't need more than 2" or 3" depth. It will eventually rot, but not in less than several years. You can also often get mulch from yard waste the city has gathered and processed for little or no cash outlay. This is often at least partially composted. The cardboard lasts 2 years and sometimes more. If you're using a longer term top layer like wood mulch, you can easily pull it back (especially in raised beds) and lay down new cardboard. If you're using something like straw, you can just lay new cardboard on top of last year's mulch when the underlying cardboard has broken down. I'd plan on doing that every 3 years or so. Then cover over with your compostable short term mulch. Do not use grass clippings as a mulch. They mat easily and will tend to shed water. You might be tempted to use shredded paper as a mulch. In most parts of the country I advise you not to try that, at least not as a top layer. It, too, tends to compress, mat, and shed water - but worse than that it is usually mostly white paper, reflects too much sun, and keeps the soil not just cool, but unacceptably cold too far into the growing season. Instead I compost it with grass clippings to balance out the high nitrogen from grass clippings. Mulching with a cardboard underlayment works well with hand watering or drip irrigation. Don't even try it if you are top watering with something like an oscillation lawn sprinkler.

Treasure, you have created a really tough situation here. Between the 2' depth, the overhang from the eaves, and the western sun, this bed will be difficult to keep enough moisture in to grow much in. I am also concerned about the house; since you built the bed almost up to the bottom of the clapboards, you have created a potential problem with any moisture in the bed being so close to the house if you decide to irrigate. Would you be willing to reconsider a redesign of the bed before thinking about plants in order to prevent structure problems with the hosue and plant survival problems?

I suppose I will have to be the first to bear the bad news.... Termites WILL eat some of your vegetable plants... The first year that I built my garden and raised beds, I planted broccoli. When they were just forming the broccoli heads, one or two fell over in the dirt. I investigated them to find out what made that happen. There were tunnels IN and through the stem! The termites had hollowed out the stem, and it had just crumpled in half. I pulled out the affected plants and saw the little rice-sized creepers scurrying away. Each day, a couple more broccoli plants crumpled over until the little buttholes had decimated every last one. Not to mention that now year 4 of growing, one of my raised beds (which sound like the same ones you (OP) built) is almost to the point of being unusable.

If you are looking for an ornamental set of raised veggie beds, look at images of parterres and adjust for making it a kitchen garden. The geometry of the garden helps make it ornamental. For instance, look at this parterre which is planted to flowers. (Sorry for the link but it won’t post with the Houzz photo button.) https://www.houzz.com/photos/summer-2012-traditional-landscape-milwaukee-phvw-vp~2864219 A similar design using low raised beds and your limestone for paved paths would be lovely. You can loosen the native soil, add a layer of compost, and then make a less deep raised bed. The veggies will send roots into the native soil as well as it will improve over time due to the compost. You don’t need to have such high bed sides. This one is planted to herbs but has shallower beds and paving between. https://www.houzz.com/photos/traditional-kitchen-garden-traditional-landscape-phvw-vp~19122726 This one has beds closer to the height I am envisioning or a bit taller, but I would keep them below a foot in height. https://www.houzz.com/photos/forest-garden-asian-landscape-san-francisco-phvw-vp~96170109 One of my neighbors had for many years a pie-shaped parterre, round with wedges. You would most likely want to remove your current bed to create your parterre so that it has a logical symmetry within the yard. Perennial veggies like your cardoon or artichoke or herbs can help with the symmetry. Grow an indeterminate tomato or beans or peas up obelisk trellises in the same spot in each bed. If the beds and certain key plants or structures are symmetrical, all the plants don’t have to be. Adding a center feature such as a bird bath or obelisk will add to the ornamental feel. It seems like your placement of the current bed to allow just enough room to mow and the dogs to run makes sense.