In a large non-stick frying pan, heat 2 tablespoons of olive oil over medium heat.
Add the minced onions and garlic, and sauté until translucent and just beginning to brown.
Add the tomatoes and sauté for 1 to 2 minutes, just enough to soften them slightly without turning mushy.
Transfer everything to a large pot or casserole that can hold all the vegetables.
Season each vegetable separately with salt and pepper to enhance their flavors.
Add 2 tablespoons of olive oil to the pan, then sauté the peppers for about 2 minutes, until they start to change color. Transfer them to the pot and stir.
Repeat with the zucchinis, then the eggplants. Sauté briefly until slightly tender, then add them to the rest of the vegetables.
Add the thyme, oregano, bay leaves, and the teaspoon of sugar, then reduce the heat to low. Gently stir to evenly distribute the vegetables and herbs without crushing them.
Halfway through cooking, stir in a generous tablespoon of tomato paste to enhance the color and flavor.