1. Preheat the oven to 180°C (350°F).
2. Grease an oval baking dish.
3. Peel the garlic cloves and onion.
4. Cut the onion and one of the 5 garlic cloves into small pieces.
5. Bake the onion pieces and the pieces of one garlic clove for 5 to 10 minutes. Then let the dish cool slightly.
6. Peel and slice the potatoes, then place them in the bottom of the dish on top of the cooked garlic and onion.
7. Wash the vegetables, then slice them into rounds of the same thickness and, if possible, the same diameter.
8. Arrange them in the dish, on top of the garlic and onion, standing upright in successive rows: tomato, zucchini, tomato, eggplant, and so on; intersperse the remaining 5 garlic cloves.
9. Season with salt and pepper, drizzle with olive oil, and sprinkle with Herbes de Provence.
10. Bake for 1 hour in a convection oven at 180°C (350°F). Then, cover the dish with aluminum foil and bake for an additional 30 minutes.
11. At the end of the 30 minutes, remove the foil and sprinkle grated cheese on top. Bake for a few minutes until the cheese is golden and bubbly.