12slices3/4-inch thick white bread, such as Texas Toast
6tablespoons85g unsalted butter
3cups720 ml whole milk
1/2teaspoonfreshly ground black pepperdivided
8ouncesgrated Gruyère cheese divided
1/4cup60 ml Dijon mustard
10ouncesask deli for 12 thin slices Black Forest ham
Arrange racks in top and middle of oven; preheat to 375°F.
Arrange bread slices in a single layer on a baking sheet and bake, flipping once, until dry to the touch but not toasted, 5–10 minutes. Using a 2″ round cookie cutter or sharp paring knife, cut a hole in the center of 6 bread slices. Set aside.
Melt the butter in a large pot over medium heat. Add flour and cook, whisking constantly, until butter is light gold and thickened, about 3 minutes. Slowly add milk, whisking constantly to prevent lumps from forming. Increase heat to medium-high and cook, whisking, until mixture thickens and coats the back of a spoon, 4–6 minutes. Reduce heat to low. Add 3/4 tsp. salt, and 1/4 tsp. pepper into the sauce.
Add 1 cup Gruyère a handful at a time, making sure cheese is melted before adding more.
Coat a 13×9-inch casserole dish with cooking spray. Spread one-third of the Béchamel sauce in the dish. Spread Dijon mustard onto the six whole pieces of bread (the ones without holes). Arrange pieces in a single layer in the dish on top of the sauce. Top each with 2 slices of ham, folding to fit on bread if necessary.
Spread another third of the Béchamel over ham. Sprinkle evenly with half of the remaining Gruyère cheese. Place 6 bread slices with holes on top to form 6 sandwiches. Spread remaining Béchamel over sandwiches, avoiding the holes. Sprinkle with remaining Gruyère, also avoiding the holes. Crack 1 egg into each hole. Season with remaining 1/2 tsp. salt and 1/4 tsp. pepper.
Spray a large piece of foil with nonstick spray. Place the foil oiled side down over the baking dish. Crimp to seal the edges. Bake on middle rack for 20 minutes. Remove foil, increase oven temperature to 400°F, transfer dish to top rack, and bake until egg whites are just barely set and yolks are still runny (eggs will continue to cook slightly when removed from oven), 12-15 minutes. Let cool 10 minutes before serving.
I added bake time to cook the eggs through. This took about 20 minutes on the top rack. I would recommend keeping a watchful eye on the eggs during the final bake so you can best gauge doneness.