Preheat the oven to 400 degrees F.
Melt the butter over low heat,add the flour stirring for 2 minutes. Slowly pour the milk into the butter–flour mixture and cook, whisking constantly, until the sauce is thickened. Remove from heat,add the salt, pepper,1/2 cup grated Gruyere, and the Parmesan and set aside.
Slice the croissants and toast lightly in hot oven.
Lightly brush one half of a croissant with mustard, add a slice of ham & egg to each, and sprinkle with half of the remaining Gruyere. Top with another piece of toasted bread. Spoon the tops with the cheese sauce, sprinkle with the remaining Gruyere.Turn oven to broil and broil for 3 to 5 minutes, or until the topping is bubbly and lightly browned. Serve hot.