1. Butter one side of each slice of bread
2. Divide the ham and cheese evenly on the non-buttered side of bread
3. Place another slice of bread on top of the ham and cheese, so that both buttered sides are facing the outside
4. Griddle the sandwiches until golden brown and crispy on both sides (about 3 minutes on each side)
5. Spread the béchamel generously on the top of each sandwich and place under broiler. Cook until it is brown and blistered.
6. Cook the eggs sunny side up and place 2 eggs each on top of the béchamel
Directions for Bechamel Sauce
1. Melt butter with peppercorns, onion, bay leaf, and salt. Once butter has melted, add the flour and cook until it is a light brown.
2. Add milk and whisk to combine.
3. Bring to a simmer while using a spatula to scrape the bottom of the pot to avoid sticking.
4. Add the grated nutmeg . Simmer until starch is cooked out and strain.