Heat a little olive oil in a pan and braise the onions for 5 min. Add the garlic and saute another 2 min. Drain the grease.
Add the chopped eggplant and a little more olive oil and braise for 5 min.
Pour in the remaining olive oil and braise the zucchini. Take them out. Put the garlic and tomatoes in a pot, add the bay leaves and thyme, a little salt and black pepper.
Saute until the tomatoes soften. Put the vegetables back in with the tomatoes and saute another 15 min. Serve right away.