1. Preheat broiler. Heat a large ovenproof skillet over medium-high heat. Butter bread on all sides, and top 2 of the slices with ham and, if desired, a smear of Dijon. Top with 1/2 cup cheese, and cover with remaining bread slices. Place sandwiches in skillet, pressing gently with back of spatula. Let cook about 1 to 2 minutes or until bottom is lightly golden.
2. Top sandwiches in skillet with Mornay Sauce and remaining 1/2 cup cheese. Place skillet in oven, and broil 2 to 3 minutes or until golden and bubbly, taking care not to burn. Top with egg, and serve immediately.