Preheat your oven to 375°F (190°C).
Boil the eggs for 15 minutes in simmering water.
Then, transfer them to cold water for easy peeling.
Remove the shells and set aside the eggs to cool.
In a saucepan, melt 2 tablespoons of butter over medium heat.
Stir in the flour to make a roux, and cook for 1-2 minutes.
Gradually whisk in the milk to create a white sauce.
Cook until thickened, then season with salt and pepper to taste.
Separate the egg whites and yolks.
Chop the egg whites and set aside.
In a bowl, cream the egg yolks with the heavy cream.
Add the creamed yolks to the white sauce, then stir in the chopped egg whites and chopped parsley.
Pour the mixture into a baking dish.
Sprinkle bread crumbs and diced butter over the top.
Bake in the preheated oven for 15-20 minutes, or until the top is golden brown and the sauce is bubbly.
Serve your creamy baked eggs hot and enjoy!