Prepare Croque-Monsieur. When the sandwiches are almost golden, remove from the broiler and use a paring knife to cut a small round out of each top piece of the cheese-covered bread, exposing the ham. Reserve the rounds. Break 1 small egg into each hole and place under the broiler until the eggs are set, 2 to 3 minutes (you may need to move the sandwiches farther from the broiler so the eggs cook before the cheese burns). To serve, top the eggs with the cheese-covered rounds.