Preheat your oven to 400°F (200°C).
Butter one side of each slice of bread and place them buttered side down on a baking sheet.
Spread mustard on the unbuttered sides of the bread.
Place a slice of ham and a slice of cheese on each piece of bread.
Close the sandwich by placing the two halves together, buttered sides out.
Bake in the oven for about 6-8 minutes, or until the bread is toasted and the cheese is melted.
While the sandwich is baking, fry an egg in a small skillet until the white is set but the yolk is still runny.
Place the fried egg on top of the sandwich, season with salt and pepper, and serve immediately.