I'm also very high up on the no food waste side if life. Very little actually makes its way to the compost heap.
We've taken to eating broccoli stems, cauliflower leaves and stems and so on. I didn't know previously that they were edible
As for food leftovers, there rarely are any because wer actually don't eat that way. Wer only cook what we'll eat that meal in the way of veg. For main items, say veg lasagne, I've always done it so that there are x many portions. Got instance the lasagne dish hold 6 portions. The other dishes hold 2 generous or 3 average sized portions. So we'll eat veg lasagne for 2 days in a row, served with different side items, and the 3rd pair of portions are frozen (on day 1 once cold) and cut into single portion size. That is your portion, end of story. Soup is usually cooked in the morning, so is divided up by evening (cooked in am because that's when my back is away it's best for standing). I just get out the containers I know the size of, 1 portion or 2 and divide the soup up. It can be made to make a set many portions and if there's a touch over, hubby just gets a little more on day 1. So there's never food left over or going to waste. My chickens see none if it (though they do love cauliflower leaves). Even pumpkin and squashes in general are eaten with the skin on. I never peel anything if it says to. So potatoes are always with skins on, even with mash. My chickens do get banana skins which they adore.
Any vegetable or fruit waste does make its way to the compost tumbler. One advantage of being in Australia is that it stays warm in there so it decomposes quickly. But I still cut things up. Celery leaves are currently my biggest waste item. Celery comes with its leaves on here and we get 2 a week. My chooks won't eat them, so it's too the compost heap for them.