Preheat oven to 350.
To make Mornay sauce:
In a small saucepan, melt butter. Add flour and stir until fragrant.
Gradually whisk in milk, salt, pepper, nutmeg
Bring to a simmer, whisking constantly and cook until thickens
Remove from heat and stir in gruyere, let cool
To make sandwich:
In an ovenproof skillet over medium heat, toast bread until golden on both sides
Spread 1/2 tbsp butter on each slice, then flip over 2 slices and spread wach with 1 tsp mustard and 1tbsp mornay sauce
Add to mustard slice 3 slices ham, 1/4 cup gruyere cheese, and remaining bread slices.
Spead tops with 2 tbsp sauce, and sprinkle with remaining gruyere
Transfer skillet to oven and cook 15-18 minutes, until cheese is melty and top is golden
To make egg:
In a nonstick skillet over medium-high heat, melt butter
Crack eggs into skillet and fry until whites are set
season with salt and pepper, and add to the top of each sandwich
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