Bit too late for the event, I guess. Just for the record, I never use green peppers, red ones instead.
Perhaps you know all that, but I'll mention it anyway: the eggplant, I slice them, put salt between the slices and let them rest for 15-30 minutes (preferably with a heavy pot on top to weigh them down). Then remove the liquid that came out of the eggplant, optionally rinse out the salt, and dice them. As a result they cook quicker and more evenly.
Finally I put all together in the pot (including lots of large pieces of onion), olive oil, no added water and stew the whole lot. Spices/herbs are a bonus but it tastes lovely even without.