Preheat the oven to 300 degrees and begin to melt the butter in a small saucepan.
Slowly whisk in the flour and then the milk. Continue to whisk at low heat until it becomes a thick sauce. Then pour into a bowl and set aside.
Toast the bread if desired (or you can let it become a desired golden in the oven later). Layer both pieces of the bread with a thin covering of the creamy mixture on the inside.
Next, put on two thick slices of ham and a slice of cheese.
Place in oven until the cheese has melted.
While it's in the oven, fry the eggs to the desired preference.
Top with one last layer of the creamy mixture and an egg and enjoy!