Step 1

Heat the oven to 400°F with a rack in the middle position. In a small bowl, whisk together the crème fraîche, mustard, nutmeg and ¼ teaspoon each salt and pepper. Stir in the cheese; set aside. Divide the ham into 4 stacks to make portioning easier.

Step 2

Spread one side of each of 8 slices of bread with the butter, dividing it evenly. Place 4 slices, buttered side down, on a broiler-safe rimmed baking sheet, then spread 1 tablespoon cheese mixture onto each. Top each with half of a ham stack. Place a slice of unbuttered bread on top of each ham layer. Repeat the layering of 1 tablespoon cheese mixture onto each sandwich, followed by the remaining ham, then top with the remaining buttered bread, with the buttered sides facing up. Bake for 10 minutes.

Step 3

Using a wide metal spatula, flip each sandwich. Bake until the tops of the sandwiches are lightly browned, 7 to 9 minutes.

Step 4

Remove the baking sheet from the oven; heat the broiler. Spread each sandwich with the remaining cheese mixture, dividing it evenly. Broil until the surfaces are bubbling and spotty brown, 1 to 1½ minutes. Transfer the sandwiches directly to a cutting board and cool for about 5 minutes. Cut each sandwich in half, then serve.