Prep the eggplant:
Sprinkle the eggplant cubes with ¼ tsp of salt and place them in a colander set over a bowl. Cover with a paper towel, top with a plate, and weigh it down with a heavy can. Let drain for about 30 minutes to draw out any bitterness. Rinse the eggplant and pat dry with paper towels.
Cook the onions and garlic:
Heat 2 tbsp of olive oil in a medium skillet over medium heat. Add the onions and ¼ tsp salt. Cook for about 3 minutes, until softened and translucent. Stir in the garlic and cook for another 1–2 minutes, until lightly browned. Transfer the onion and garlic to a Dutch oven or large casserole dish using a slotted spoon.
Sauté the peppers:
Add 1 tbsp olive oil to the skillet. Stir in the red peppers with a pinch of salt and cook for about 7 minutes, until just starting to brown. Transfer to the Dutch oven.
Sauté the zucchini:
Add the zucchini to the same skillet and cook for about 4 minutes, until lightly golden. Transfer to the Dutch oven.
Cook the eggplant:
Add the remaining 1 tbsp olive oil to the skillet. Cook the eggplant, stirring occasionally, until lightly browned. Transfer to the Dutch oven.
Deglaze with tomatoes:
Add the chopped tomatoes to the skillet, scraping up any browned bits from the bottom. Pour the tomatoes into the Dutch oven along with the thyme and black pepper.
Simmer:
Bring the mixture to a gentle simmer. Cover and cook, stirring occasionally, for about 45 minutes.
Finish and serve:
Remove the lid and cook uncovered for another 15 minutes, until the vegetables are soft and the sauce has thickened. Stir in the basil and parsley. Serve warm or at room temperature with a drizzle of olive oil.