Dice the onion, mince the garlic. Dice the red and yellow bell peppers into 1-inch pieces. Dice the eggplant into 1-inch cubes. Dice the zucchini into 1-inch cubes. Ensure all vegetables are uniform in size for even cooking.

Heat 2 tablespoons of olive oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the chopped onion and cook until softened and translucent, about 5-7 minutes. Add the diced bell peppers and cook for another 5 minutes until slightly tender.

Stir in the minced garlic and cook for 1 minute until fragrant. Add the diced eggplant and zucchini. Drizzle with the remaining 1 tablespoon of olive oil. Sauté for 8-10 minutes, stirring occasionally, until the eggplant and zucchini begin to soften and slightly brown.

Stir in the tomato paste and cook for 1 minute, stirring constantly to deepen its flavor. Pour in the canned diced tomatoes (undrained) and vegetable broth. Add the dried thyme (or fresh sprigs) and bay leaf. Season with salt, black pepper, and the optional sugar to balance the acidity of the tomatoes.

Bring the mixture to a gentle simmer. Reduce the heat to low, cover the pot, and let it simmer for 30-45 minutes, or until all the vegetables are very tender and the flavors have thoroughly melded together. Stir occasionally to prevent sticking and ensure even cooking.

Remove the bay leaf and any fresh thyme sprigs. Taste and adjust seasoning as needed, adding more salt or pepper if desired. Stir in the fresh chopped parsley just before serving for a burst of freshness.