Either the food processor or the toaster oven.

The food processor will chop meat and nuts, shred veggies, grate cheese and veggies, slice veggies, puree soups, make emulsions, and knead dough. With additional attachments it can whip, blend, and juice, though at some point you get attachment clutter. I like Cuisinart myself.

The toaster oven will broil veggies and meat, roast/bake anything (even a small chicken), and toast bread of course, and it doesn't require pre-heating or warm up the kitchen. People love their Brevilles, I like my Krups. There are combination microwave-toaster ovens too, but I don't know how well they work.

For an appliance, the food processor. For a gadget, I love my micro plane for zesting, grating, etc. The most multi-functional item in my kitchen is me with my fab Shun 7" santoku. It's new and very sharp.

I use the food processor almost daily, I would never be without one. I have a blender and use it frequently, but I could live without it IF I had an immersion blender. I have a toaster oven, and while I don't use it as often as the blender, I wouldn't be without it.

We love our mandoline! This link is very similar to the one I have. And, like you, I don't have a pantry, except the one I use down the hall. This great tool fits in the drawer under the cooktop! Very compact.

Here is a link that might be useful: mandoline

Food processor
Toaster Oven
Veggie steamer
Rice Cooker

No particular order. But Toaster Oven has been a relatively recent addition and it's completely changed the way we eat (breakfast, especially).

Aside from that, toaster oven has doubled as heating mat for seed-starting :-) (Suspended seed pellets ~2.5 inches over the oven and germinated).

Eight inch chef's knife.

I have room for whatever I want, but I think I'm going to get rid of my crockpot. It's very big, and with my new kitchen it has lost all allure.

My mother has a teeny tiny kitchen, but even with the tiny counters there's a KitchenAid mixer and a Cuisinart.

An immersion blender is more multi-purpose useful than a motor mounted jar blender.

I have a number of specialized cutting tools and gadgets, but they don't take up much room. I inherited an electric skillet which I've never used. I may send it to my studio for melting wax. I only use my toaster oven for toasting, and could easily give it up. I love my automatic egg cooker (had one of those growing up), but it's getting a little beyond its age, and I don't really need it. I have a jar blender which I haven't taken out of the box since moving into my new kitchen a year ago.

My list is POST new kitchen though. In the old kitchen, I used the toaster oven much more. I couldn't boil eggs without the egg cooker. I needed the crockpot, and some of the others. Be careful before you downsize. Especially, keep in mind what you might need for a temporary kitchen when you are ready to remodel.

Maybe you should box up the things you don't think you need and relocate them to the garage or somewhere out of your way. Then you can see if you really don't need them, or go get them if you want them, and have them for the eventual temporary kitchen.

Breville Convection Toaster Oven. I could not have gotten through the remodel without this. It is a small but true convection oven -- big enough for a 13 inch pizza. It is a toaster (slower than a real toaster but still works fine). It bakes, broils. I think if I had two of these plus the outside Green Egg I would never need a regular full size oven. I would not say it is truly multifunctional the way a speed oven is, but it is very versatile and packs a lot of function for its size.

Kitchenaid mixer. I use the attachments to grate, slice, and even ground meat. Then my food processor and immersion blender. LOVE!

I think it's me.

My husband. :)

Definitely the immersion blender - I got rid of the big one, the food processor, and the love of my kitchen, my Magic Bullet which I use every single day.