Preheat oven to 350 degrees F. In a large bowl, combine eggs, milk, the 1/3 cup ketchup, and the 1 teaspoon mustard. Stir in ground beef, oatmeal, onion, salt, and pepper; mix well. Gently press mixture in an ungreased 9x5x3-inch loaf pan or shape into a loaf on a rimmed baking sheet. Bake for 30 minutes. Drain off fat.
After 30 minutes of baking, spoon the barbecue sauce evenly over the meatloaf. Bake for 30 to 45 minutes more or until a thermometer registers 160 degrees F. Let the meat loaf stand for 15 minutes. Drain off fat. Carefully slice meatloaf and use a spatula to transfer to a serving platter.