Preheat oven to 200C. Place 4 slices of bread on an oven tray and spread evenly with mustard. Top with ham.
Make the bechamel sauce: melt the butter in a saucepan on high and stir in flour. Cook for 1 min. Remove from heat and stir in the milk. Return to heat and cook, stirring until sauce boils and thickens. Season to taste.
Spread half the sauce evenly oven the ham. Cover with the remaining bread slices and top with the remaining sauce. Sprinkle with cheese.
Bake in the oven for 12-15 mins until lightly golden.
Meanwhile, heat a lightly greased frypan and fry the eggs for 2-3 mins until set. Top each sandwich with an egg.