1. Cook the vegetables in a pan with 2 tablespoons of olive oil.
2. Sauté the ground beef in a tablespoon of olive oil, season with salt and pepper.
3. Cook the lasagna sheets according to the instructions on the package.
4. Preheat the oven to 210°C (410°F).
5. Reduce the cream by half with salt and pepper.
6. Add the crumbled Parmesan and goat cheese; mix well.
7. Place a lasagna sheet in 4 buttered gratin dishes (or cover the bottom of a large dish). Cover with ratatouille, sautéed meat, and another lasagna sheet.
8. Pour the goat cheese sauce over the lasagna.
9. Bake for 20 minutes.
10. Optionally, garnish with a few basil leaves and serve immediately.