In a medium saucepan over medium heat, melt 4 tablespoons of butter until bubbly and golden. Whisk in 1/4 cup of flour, stirring continuously for about 2 minutes to form a roux. Gradually pour in 2 cups of whole milk, whisking constantly to avoid lumps. After thickening for about 5-7 minutes, stir in 1 tablespoon of Dijon mustard, a pinch of nutmeg, and season with salt and pepper to taste, then set aside.

Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish with butter or cooking spray. Layer evenly 6 cups of cubed stale brioche at the bottom, followed by 8 ounces of turkey ham (or veggies for a vegetarian option) and 2 cups of grated Gruyère cheese. Pour the prepared béchamel sauce over the layered ingredients, ensuring everything is well coated.

Place the Croque Madame Casserole in the preheated oven and bake uncovered for 30-35 minutes. Keep an eye on the dish—a golden brown and bubbly top is the perfect indicator that it’s nearly finished.

With 10 minutes left of cooking time, carefully crack 4 eggs on top of the casserole, placing them gently to avoid breaking yolks. Return the dish to the oven and continue baking for another 10 minutes.

Once baked, remove the casserole from the oven and let it cool for a few minutes before slicing. Serve the Croque Madame Casserole warm.