Spread mustard evenly on each of 4 slices of bread; top evenly with ham and 2/3 of the cheese. Set aside. Melt 3 tbsp. butter in a small saucepan over medium-low heat; whisk in flour and cook 3 min. Whisk in milk; bring to a boil, whisking constantly. Reduce heat to low; simmer, whisking occasionally, 5 min. Whisk in salt, pepper, nutmeg and remaining cheese until cheese is melted; remove from heat. Spread 1 1/2 tbsp. sauce evenly on the remaining slices of bread; sandwich with other halves. Melt 1 tbsp. butter in a nonstick skillet over medium-low heat; cook sandwiches until golden (3-4 min.), turning once. Move to a baking sheet; spread 1/3 cup sauce on the top of each hot sandwich. Broil sandwiches until sauce is bubbling and golden in spots (2-3 min.). While sandwiches broil, melt remaining butter in the skillet over medium heat until foam subsides; crack eggs into skillet, seasoning with salt and pepper. Cook eggs, covered, until whites are just set and yolks are still runny (about 3 min.). Top each warm sandwiches with an egg; serve immediately.