Preheat the oven to 180°C (approximately 350°F).
Rinse the zucchini and cut lengthwise into 3-4 mm thin slices. Blanch in boiling salt water for about 1-2 minutes. Rinse in cold water and drain.
Peel and finely chop the garlic and shallots. Saute in hot oil. Remove from the heat, mix in the thyme and add to the ground beef. Mix well with 2 eggs and 40 grams (approximately 2 ounces) of parmesan. Season with salt and pepper. Place a tablespoon of the beef mixture on each zucchini slice and roll. Place the rolls in the baking dish.
Mix the remaining eggs with the remaining parmesan, cream, broth and creme fraiche until smooth. Season with salt, pepper and nutmeg. Pour the sauce over the zucchini rolls so they are barely covered. Cover with cheese slices and bake for about 45 minutes. Serve hot.