1Preheat oven to 350 degrees F (175 degrees C). Butter a 9-inch square baking dish.
2Arrange eggs, cut-side down, in the prepared baking dish.
3Melt butter in a saucepan over medium-low heat. Whisk flour into the melted butter until dissolved, 2 to 3 minutes. Gradually stir half-and-half into flour mixture until sauce is thickened and smooth, about 5 minutes. Season sauce with salt, pepper, garlic powder, and mustard. Stir Gruyere cheese into sauce until melted and smooth.
4Pour sauce over eggs and sprinkle Parmesan cheese over sauce.
5Bake in the preheated oven until bubbling and golden brown, 20 to 25 minutes.
Aluminum foil helps keep food moist, ensures it cooks evenly, keeps leftovers fresh, and makes clean-up easy.