In a saucepan, add the flour and butter for the béchamel sauce. Whisk 2-3 minutes, or until you smell a nutty aroma. Add the half/half and stir until it thickens. Next, lower the heat to a simmer and add the bay leaf and grated parmesan cheese. Keep warm for service.
Add 2 slices of ham to each piece of bread and top each slice with about 1/4 cup each of grated Gruyere cheese.
Heat pan on medium high, add butter and grill each slice of bread until they are golden brown on the bottom, about 3-4 minutes.
Place each piece of bread in a toaster oven, and brown & melt the cheese on top.
Melt another teaspoon butter in omelet pan. Fry one egg, sunny side up, until done to your liking.
Assemble the sandwich by topping the two slices together, then add the fried egg and béchamel sauce. Garnish with chopped chives, cracked pepper and French sea salt. Enjoy!