What kind of material are you talking about? I have a few worm bins and I put kitchen scraps in there. I also will tear cardboard up into about 5" pieces and they take care of that pretty good.

Last year I had black soldier fly larvae and they ate all sorts of kitchen scraps in no time.

I throw leaves and pine straw into the chicken run and its incredible how fast that breaks down. I have 8 chickens and I threw two large garbage bags of pine straw into their 5'X12" run a couple of weeks ago. Its almost gone already. I gave them another bag full yesterday.

Just about everything plant-based that I can lay hands on goes into my compost. The really resistant stuff is the cardboard (torn down to pieces around the size of the side of a cereal box), and intact green leaves on their twigs (about the thickness of a pencil is where I cut it off). Longer grass clippings take a bit longer than I'd like, but they mix with the other stuff easily regardless, so I'm none too concerned with them.

Time is a wonderful shredder. If you make a pile and forget about it while making another pile which you then forget about while making a third pile, and so on, you'll come back to the first pile and find it has shredded itself give or take a few large twigs. These go into the new pile ......... Once the cycle is up and running time taken for any individual heap to compost doesn't matter.

"big pieces in the pile are a pain in the posterior to turn.
My available time and energy won't let me do too much manual shredding"

Then don't do either one. Shredding and turning are what you do when you're in a hurry. In recognition that gardening is long-term, and that one is always are planning for next year, just do what the above poster said, exactly, and everything will be just fine. It's only organic materials breaking down, and that's gonna happen whether you follow all the absurdly complicated rules or whether you just let it be.

I tend to wet my cardboard and paper before tearing up. I like to keep it out during rain but this summer was so dry that I was soaking it in 5 gallon buckets. Wet cardboard doesn't only seem to tear easier when soaked but also seems to break down faster.

How big are these "big pieces"? Are we talking about thumb-sized twigs, branches the size of a NFL lineman's thighs, or entire logs? If you accept that the entire pile will not be "done" at the same time, it gets easier.

I dump in twiggy material (thumb-sized or smaller) and if it isn't done when I sift the pile, it gets dumped in to the next pile. Eventually it will decompose.

I don't try to compost anything from kindling size and up, I give it to people who need firewood.

The big pieces are chunks of cardboard about the size of a cereal box side, rarely an intact pizza box, and the roughly pencil width twigs that are left in there as intact as they come off the larger limbs.

Wood thicker than that gets set aside, except for the odd branch I use as a spacer for air and water flow in mat-prone material. When I have a substantial pile of wood, I burn it to ash and sparingly apply it to gradually neutralize this acidic soil.

I don't turn compost ... I have a pile it and forget it system, so the only time I have to mess with "large" pieces is when I sift the pile. If it falls through the sifter, it's "done" and if it makes it to the exit, I toss it in the newest bin to keep composting.

This batch was very twiggy because it was a;; "browns" - yard clean-up raking and trimming after several years of no maintenance at all. I just tossed all the stuff into a bin and left it for a couple of years, then watered it to decompose as much as possible.

The newer bins have more kitchen scraps and urine-soaked sawdust from the litter pans so they are decomposing much faster.

No-turn composting

My DIY sifter

Eventually I'd like to use a pile and let it rot approach, but that doesn't suit my needs right now.

I have a lot of heavily compacted (as in, buckled the steel of a manual tiller before the soil would let go), sometimes poisoned clay that I'm trying to open up enough to work and to drain, and revive the soil food web enough for continual improvement during the growing season. I want it ready by February. I started with no compost or even healthy soil a few months ago, and I'm doing what I can before it freezes here. If possible, I'll keep it going during the freeze, but I don't know if I can manage it.

I did see a good sign the other day. I think I startled my lady. I don't think she expected me to rush into the house excited with a handful of bugs.

Those are the wrong size and color to be descended from the few euros I dropped in, and they're IN THE CLAY, not the developing compost sitting atop it. Field of Dreams effect is working! :D

"I have a lot of heavily compacted clay. I want
it ready by February."

Heavy mulching and composting right over the top of the clay can do it. I had hard-packed alkaline desert dirt - hard enough that I had to use a mattock to dig planting holes for 6-pack seedlings - and turned it into a veggie bed I can dig in with a hand trowel.

1. Drip lines under everything for even moisture.

2. Fertilized well with ironite and soil sulfur (we're short on iron and high on pH)

3. Fertilized lightly with ammonium nitrate (both were sprinkled on the dirt, not even raked in)

4. Spread layer of whatever compost and other material I had about 4 inches deep. Did not till it in.

5. Dug holes and planted veggies (okra and eggplants)

6. Spread a thick (4-6 inch) layer of wood chips as mulch.

Okra has an astounding root system, going down 4-6 feet, so at the end of the season when I sliced off the plants at the base, it left a large amount of organic material in the dirt far deeper than I could dig. Repeated for the next year, adding compost as it became available, adding mulch as it decomposed, enlarging area as well.

I had the advantage of a mild climate, but the freeze-thaw cycle in a cold climate does a lot to destroy plant material. And there are cold-tolerant fungi and bacteria active then.

Amend whatever you can amend really well, and add onto the amended area as materials allow. it's better to amend thoroughly than to skimp over a larger area.

I found a picture of the first year ... the plants were loving it.

https://www.flickr.com/photos/38617480@N07/3614575147/in/photostream/