Spread each slice of bread with Dijon mustard on one side and the softened butter on the other. With the mustard side facing up, layer a slice of swiss, turkey, ham, and top with another slice of swiss.
Top each with the remaining bread slices, buttered-side up. Press down on the sandwiches to set.
In a wide, shallow dish (like a pie plate) combine the cream, eggs and pepper, using a whisk. Set aside.
Heat a large, heavy-bottomed sauté pan or griddle over medium heat. When the pan is ready, dip the sandwiches in the cream mixture to coat well. You will have bits of egg clinging to the bread's surface.
Cook the sandwiches for 3 - 4 minutes on each side or until browned and crisp. Serve immediately.