Croque Madame | Ham, Cheese & Egg Sandwich

Ingredients

• 2 tbsp unsalted butter
• 2 tbsp all-purpose flour
• 1 1/2 cups milk, tempered
• 1/4 tsp freshly grated nutmeg
• 1/4 tsp kosher salt
• pinch of white pepper
• 1/4 cup grated Gruyère cheese
• 1/4 cup grated Parmesan cheese
• 8 pieces bread (preferably something like Brioche or Italian)
• 8 to 16 pieces plain ham (1 or 2 per sandwich)
• 1 to 2 tbsp Dijon mustard
• 2 cups grated Gruyère cheese
• 2 tsp unsalted butter
• 4 large eggs
• kosher salt (to taste)
• freshly ground black pepper (to taste)