Preheat the oven to 350 degrees F (175 degrees C). Butter a 9 inch square baking dish.
Melt butter in a saucepan over medium low heat. Add flour and whisk until dissolved, 2 to 3 minutes. Gradually add half and half and whisk until sauce is thick and smooth, about 5 minutes. Season with salt, pepper, garlic powder, and mustard. Stir in Gruyère cheese until melted and smooth.
Arrange eggs, cut side down, in the prepared baking dish. Pour sauce over eggs and sprinkle with Parmesan cheese.
Bake in the preheated oven until bubbly and golden brown, 20 to 25 minutes.
Hard-Boiled Egg Casserole · Dinner Match Lab | Dinner Match Lab