Preheat the oven to 375°F (190°C). Lightly oil a 9x13-inch baking dish.
Slice the zucchini, eggplant, and tomatoes into even 1/4-inch rounds. Sprinkle the eggplant slices with salt and let sit for 10 minutes to draw out moisture; pat very dry with paper towels.
Fry the zucchini: heat about 2 tablespoons of olive oil in a large skillet over medium-high heat. Cook zucchini slices in a single layer for 2–3 minutes per side until golden. Transfer to a paper towel–lined plate. Repeat in batches, adding more oil as needed.
Fry the eggplant the same way, cooking in batches until golden on both sides and slightly tender. Drain on paper towels.
Make the sauce: in the skillet (wipe out excess oil if needed), warm 2 tablespoons olive oil over medium heat. Add diced onion and cook until softened, about 4–5 minutes. Stir in tomato sauce, tomato paste, herbs de Provence, dried basil, and sugar (if using). Season with salt and pepper and simmer 3–5 minutes.
Spoon a thin layer of the tomato sauce into the bottom of the baking dish. Arrange the fried zucchini, eggplant, and tomato slices in overlapping rows. Sprinkle minced garlic over the top and season lightly with salt and pepper. Drizzle with a little olive oil.
Cover tightly with foil and bake for 40 minutes. Remove foil and bake 10–15 minutes more, until the top is lightly caramelized and the vegetables are tender but still holding their shape.
Let rest 5 minutes. Finish with fresh basil and (optional) grated Parmesan. Serve warm.