Preheat the oven to 375 degrees . Arrange the bread on a baking sheet and spread a thin layer of fig spread on each slice. In a small skillet, melt 2 tablespoons butter over medium heat. Whisk in the flour for half a minute, then whisk in the milk. Season the sauce with salt, pepper and nutmeg. Turn off the heat and stir in the mustard.
Divide the sauce among the bread slices. Top each slice with 2 folded prosciutto slices and a small mound of fontina, scattering the cheese all the way to the edges of the bread. Bake until golden, 10 to 12 minutes.
Rinse out the skillet and return to the stove. When the sandwiches are done, cook the eggs to order in pats of melted butter.
Top each sandwich with an egg and serve.