Sounds delish, hm? I figured I'd miss our dishwasher (and I do), but I never thought much about missing the garbage disposal. Trash is separated out here into a number of different categories, one of which is burnable. I guess it isn't any different than having a compost pile (although that would be decidedly less stinky), but all of our food scraps and bits of paper all go into our burnable bin.
Built into our kitchen sink is a metal bucket with holes in it, so when prepping a meal, peelings and such can just get tossed in the sink. The food will get caught in the bucket and liquids are still able to pass through the holes. When the bucket gets full, it can be lifted out and dumped into the burnable bin. Thankfully A turned us on to mesh bucket liners, which make the emptying process a bit neater and easier.