Preheat oven to 180 degrees C. Coat a small and low-sided baking dish with butter. Crack eggs into a bowl, season with salt, add basil and beat with a whisk or fork.
Grate zucchini on a fine grater as well as 2/3 of the cheese, mix with the egg mixture.
Coat a small baking dish with butter. Pour the egg mixture, arrange tomato slices on top, season them with salt. Sprinkle the casserole with the remaining grated cheese.
Place in the oven and bake for approximately 20 minutes or until the mass sets. Serve seasoned with freshly ground pepper and sprinkled with basil leaves and - optionally - drizzled with extra virgin olive oil.