Preheat your oven to 356°F (180°C).
Melt 1 tbsp of butter in a small pot over medium heat. Once melted, add 2 tbsp of flour and stir with a wooden spoon or spatula to form a roux.
Let the roux cook for 2-3 minutes, then season with salt, pepper, and Herbes de Provence, if desired.
Gradually add ⅔ cup of milk, a little at a time, allowing the roux to fully absorb each addition before adding more. Stir continuously until the sauce is smooth and creamy.
Place two slices of bread on a baking tray. Spread a few tablespoons of the béchamel sauce on each slice.
Layer one slice of ham and ¾ cup of the grated cheese (about half of the cheese) on top of the sauce.
Cover with the remaining 2 bread slices and top with more béchamel sauce and the rest of the cheese.
Bake the sandwiches in the preheated oven for 20 minutes, or until the cheese is melted and golden brown.
While the sandwiches are baking, fry two eggs sunny-side-up in a pan.
Once the sandwiches are ready, place a fried egg on top of each one. Serve immediately and enjoy!