In a saucepan over medium heat, melt 3 tablespoons of unsalted butter.

Add 1/4 cup of plain flour to the melted butter and whisk to create a roux, cooking for about 1-2 minutes until it bubbles lightly without browning.

Gradually whisk in 1 cup of milk and 1/2 cup of cream, stirring until the sauce thickens, about 5-7 minutes.

Sprinkle in 1/2 teaspoon of salt, 1/4 teaspoon of white pepper, and 1/4 teaspoon of nutmeg, then remove the saucepan from heat.

Preheat your skillet over medium heat and add 2 tablespoons of unsalted butter until it starts to foam.

Spread 2 tablespoons of Dijon mustard on one side of each slice of sourdough bread.

Layer 4 slices of Swiss or Gruyere cheese and 4 slices of ham on the unbuttered side of two slices of bread. Top with the other slices, mustard side down.

Place the sandwiches in the skillet and cook until both sides are golden brown and the cheese is gooey, about 3-4 minutes per side.

Remove the sandwiches from the skillet, place them on a baking sheet, and sprinkle 1 cup of shredded Gruyere cheese and 1/4 cup of grated Parmesan on top.

Broil for about 2-3 minutes until the cheese is bubbly and golden.

Carefully remove from the oven and serve immediately.