Preheat your oven to 375°F (190°C).
Grease a baking dish with butter.
Spread the fresh butter evenly over the bottom of the baking dish.
Sprinkle half of the grated cheese over the butter.
Carefully crack the eggs into the dish, ensuring not to break the yolks.
Season the eggs with salt and pepper to taste.
Pour the heavy cream over the eggs.
Sprinkle the remaining grated cheese over the eggs.
Bake in the preheated oven for 10-15 minutes, or until the egg whites are set but the yolks are still slightly runny.
Remove from the oven and let it cool for a minute before serving.
Serve your Swiss-style Baked Eggs hot and enjoy the rich and cheesy flavors.