Sprinkle eggplant cubes with salt and let drain in a colander for 30 minutes. Pat dry.
Preheat oven to 350°F (177°F). Line a baking sheet with tin foil. Put eggplant cubes across baking pan, cover with 2 tbsp of olive oil and top with another sheet of tin foil secured over the eggplant. Bake until soft, about 45 minutes. Set aside with top removed.
Over medium-low heat, heat 2 tbsp olive oil in a large heavy pot. Add peppers, onion, and garlic and cook, uncovered, until wilted. About 10 minutes. Stir occasionally.
Add zucchini, baked eggplant, and herbs de Provence. Cook another 10 minutes, stirring, to blend flavors. Season with salt and pepper.
Add the diced and "crushed" tomatoes and tomato paste mixed into 1 cup reserved juices. Simmer for 30 minutes, stirring occasionally. After 30 minutes, stir in 2 tbsp oil and cook for 5 more minutes.
Stir in parsley and thyme, adjust seasonings, if necessary. Serve hot, or at room temperature.