In a small sauce pan melt 2 tablespoons of butter over medium low heat. Whisk in flour until smooth. Let bubble, don't brown. Whisk frequently for 1 minute.

Gradually whisk in warm milk(I used cream for a thicker sauce). Raise the heat to medium and bring to a boil. While whisking frequently. Reduce heat and simmer, whisk frequently until thickened. About 5 minutes.

Remove from heat. Stir in .75 cups of cheese and 1 teaspoon of mustard. Season with salt and pepper. Transfer to a bowl and place plastic wrap directly onto the surface of sauce and let cool.

Preheat oven to 400 degrees F. Line a baking sheet with parchment paper. Arrange bread slices on sheet(I placed a pat of butter on each slice). While baking turn once until toasted on both sides. About 10 minutes, remove from oven and set aside.

In a frying pan melt rest of butter. Cook the eggs and season with salt and pepper to your desire. Just make sure the egg white is cooked.

Preheat the broiler. Spread remaining mustard on 4 slices of bread. Place equal amounts of ham on bread(i used baked ham and think the thick ham would be better). Then spread cheese sauce 1 tablespoon on each slice.

After sand which is built spread more cheese sauce on top and sprinkle remaining grated cheese on top as well. Place in oven and cooked till cheese is boiling and brown. Remove and plate then put fried egg on top. And enjoy.