In a medium saucepan over medium heat, melt 4 tablespoons of butter. Whisk in 4 tablespoons of flour to create a roux, stirring for about 2 minutes until golden. Gradually pour in 2 cups of milk, continuing to whisk until the mixture thickens, approximately 5-7 minutes. Stir in 1 tablespoon of Dijon mustard and a pinch of nutmeg for added flavor. Set aside once smooth and creamy.

Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish while the oven heats. Arrange slices of slightly stale brioche neatly across the bottom of the dish, ensuring even coverage. Spoon the prepared béchamel sauce generously over the brioche, ensuring it soaks in well. Sprinkle 2 cups of shredded Gruyère cheese and 1 cup of diced turkey ham evenly on top for a delightful mix of flavors.

Using the back of a spoon, gently press down into the casserole mixture to create small divots for the eggs.

Place the casserole in the preheated oven and bake uncovered for about 25 minutes, until the cheese is bubbly and the top is golden brown. If you’re adding eggs, carefully crack 4 large eggs into the divots made earlier and return the dish to the oven for an additional 10 minutes.

Once done, remove from the oven and allow it to cool for about 5-10 minutes. Serve warm, garnished with freshly chopped parsley and a sprinkle of black pepper.