Croque-Madame Sandwiches

Today we had our 'dinner' at lunchtime since my husband will be away at dinner time.  I had always wanted to try a croque madam but have never made it before.  It was very good but very rich!  I had bread which had very large slices of bread so we all had too much to eat since it was so rich.  Half sandwiches for everyone next time;).

Croque-Madame Sandwiches

 5    Tbs. unsalted butter
2    -1/2 Tbs. all-purpose flour
1    -3/4 cup milk (whole or low-fat)
2    Tbs. brandy
2 t  Worcestershire sauce
1/4 t  fresh thyme
1/4 t  grated nutmeg
Kosher salt and freshly ground black pepper
8 sl country-style white sandwich bread
4 t  Dijon mustard
4 oz Gruyère,grated (1 cup)
12 oz leftover roasted fresh ham sliced (or substitute sliced roast pork
1/2 oz Parmigiano-Reggiano,finely grated (1/2 cup)
4    large eggs,at room temperature
Melt 2 Tbs. of the butter in a medium saucepan over medium-low heat.
Whisk in the flour and continue whisking just until it turns beige,
about 20 seconds. Whisk in the milk in a slow, steady stream; continue
whisking until smooth, thickened, and slightly bubbling, 2 to 3 minutes.
Whisk in the brandy, Worcestershire sauce, thyme, nutmeg, 1/4 tsp.
salt, and 1/4 tsp. pepper. Whisk for 30 seconds; then remove from the
heat and set aside, whisking occasionally to prevent a skin from
forming.
Position a rack 4 inches from the broiler element and heat the broiler
on high.
Spread four of the bread slices on one side with 1 tsp. Dijon mustard
each. Layer the Gruyre and ham on the bread in this pattern: cheese,
ham,  cheese. Top with the remaining bread.
Melt 1 Tbs. of the butter in a 12-inch skillet over medium heat. Cook
2 of the sandwiches until brown and crisp, turning once halfway through
the cooking, about 4 minutes. Transfer to a rimmed baking sheet. Repeat
with another tablespoon of butter and the remaining 2 sandwiches.
Ladle the bchamel sauce over the sandwiches (it will run down the
sides) , and then top with the Parmigiano-Reggiano. Broil until
bubbling and lightly browned, 3 to 4 minutes.
Meanwhile, in a 10-inch nonstick skillet, melt the remaining 1 Tbs.
butter over medium heat. Crack the eggs into the skillet and fry them
sunny side up until the whites are set but the yolks are still runny, 3
to 4 minutes.
Use a large, flat spatula to transfer the sandwiches to serving plates.
Place a fried egg on each. Sprinkle with salt and pepper and serve.