Croque Madame

This is a French grilled ham and cheese that I had at a cafe on the Champs Elysees in Paris. Marshall and Amy had the best omelets there as well, but those I find hard to re-create. If you don't have the eggs then it is a Croque Monsieur. Once again Barefoot Contessa.
2 Tbsp. butter
3 Tbsp. flour
2 c. hot milk
1 tsp. salt
1/2 tsp. pepper
pinch of nutmeg
12 oz. gruyere
1/2 c. parmesan
16 slices white bread, without crust
dijon mustard
ham
8 eggs

Preheat oven to 400 degrees. Melt butter over low heat and add all the flour; stir for 2 minutes. Pour in the hot milk slowly and whisk until thickened. Remove from heat and add salt, pepper, nutmeg, 1/2 c. grated gruyere and parmesan. Set aside.
Toast the bread in the oven on both sides. Lightly spread Dijon on half the slices of bread. Add ham and half the gruyere. Top with another piece of bread. Pour cheese sauce over the top and sprinkle with remaining Gruyere. Bake fro 5 minutes and then turn on the broiler and broil for 3-5 minutes. Fry the eggs in butter and serve over the top of the sandwiches