Prepare the Filling: In a medium saucepan, melt the butter over medium heat. Whisk in the flour to create a roux and cook for 1-2 minutes. Slowly pour in the broth and milk, whisking until smooth. Add garlic powder, onion powder, salt, and pepper, and cook until the sauce thickens, about 5 minutes.
Add the turkey and vegetables to the sauce, stirring until well combined. Transfer the mixture to a greased 9x13-inch baking dish.
Prepare the Stuffing Crust: In a bowl, combine the stuffing with the beaten egg, mixing until evenly coated. Spread the stuffing over the turkey mixture in the baking dish, pressing down gently to create an even layer.
Bake: Place in a preheated oven at 375°F (190°C) and bake for 35-40 minutes, or until the stuffing is golden brown and the filling is bubbly.
Allow to cool for a few minutes before serving. Enjoy warm!