Preheat the oven to 350 degrees.
In a large bowl, whisk together the eggs, milk, salt and pepper, and 1 cup of the cheese, and then set aside. In a small bowl, stir together the ketchup, Dijon, and Worcestershire sauce, and set that aside.
Heat the olive oil in a 10-inch, oven-proof skillet (cast iron works well) over medium heat. Add the onion and sauté 2-3 minutes until softened. Add the ground beef and cook, breaking up and stirring as you go, until the meat is no longer pink. Drain any excess grease.
Stir in the ketchup mixture until the beef mixture is evenly coated. Then add the egg mixture and make sure the beef is well distributed over the pan.
Bake for 20-25 minutes or until just set in the middle. Remove from the oven.
Top with the remaining 1/4 cup of cheese and broil, watching closely, for 1-2 minutes or until the cheese is melted and the top turns golden brown.
Serve as is, or garnish with optional toppings. Leftovers are delicious. Reheat or serve at room temperature.
