Prep the veg - slice the stem off each eggplant and cut into bite-sized pieces. Slice the celery into a small dice. Chop the onion. Mince the garlic. Chop the peppers, tomatoes, and olives.
Add the tomatoes, capers and olives - Add the tomatoes to the pan, along with 1/2 t salt and the sugar. Continue cooking until the tomatoes have cooked down and the rest of the dish is beginning to meld, another 8-10 minutes. Turn down the heat to medium and add the capers, olives, and balsamic. Cook for until the eggplant is completely cooked down, 30-40 minutes. You don't want a hint of texture in the eggplant - that's what the celery is for!
Finish - Once the vegetables have broken down and there's not much liquid left in the pan, give it a taste. I like to add a good glug of balsamic glaze at this point - up to 1/4 cup. You may want to add salt and pepper as well.