Sauce: Melt the butter in a small saucepan over medium heat. Whisk in the flour and cook, keeping it light in color, about 1 to 2 minutes. Whisk in the milk and bring to a boil, then lower the heat to a simmer. Season the sauce with salt, to taste, and cayenne and continue to cook just until thick enough to coat the back of a spoon, about 3 minutes. Stir in cheese and set aside. Preheat oven to 400 degrees F. On an aluminum foil lined sheet tray, heat the ham and toast croissants. Melt 1 tablespoon of butter in a medium nonstick skillet over medium-high heat. Add the eggs and water and cover with a lid to steam eggs over easy. Top each bottom slice of toasted croissant with a teaspoon of Dijon, then 3 slices of hot ham and 1 over easy egg. Spoon the cheese sauce over the egg and leave somewhat open faced, by putting the top piece of the croissant on the side. Garnish with parsley or chives, and serve.
If the milk is hot, it makes the recipe foolproof for a smooth sauce.