3 tablespoons unsalted butter, softened (1/2 tablespoon per slice)
Grainy or Smooth French-Style Mustard (optional)
Place on the buttered sides:
6 thin slices good-quality ham (about 2 ounces per slice)
Cover with the remaining slices of bread. Place the sandwiches under the broiler and grill until golden. Remove the sandwiches, turn, and cover each with:
4 1/2 ounces Gruyère cheese, grated
Return to the broiler and grill until the cheese is almost golden. Remove from the broiler and cut a small round out of the top piece of the cheese-covered bread, exposing the ham. Reserve the round. Break into the holes:
6 small eggs (1 egg per serving)
Place under the broiler until the egg is set, 2 to 3 minutes. Top the egg with the cheese-covered round. Cut into halves or quarters and serve warm.