Add the three meats and all of the other ingredients (except the tomato sauce) to the bowl with the milk-soaked bread. With a gloved or bare hand, mix everything well to combine.
1 pound ground beef, 1 pound ground pork, 1 pound ground veal, 2 Tablespoons parsley, 2 Tablespoons basil leaves, 1 teaspoon dried oregano, 1 Tablespoon onion powder, 1 teaspoon garlic powder, 2 teaspoons red pepper flakes, 2 Tablespoons kosher salt, 1 teaspoon black pepper, ¼ cup Parmesan cheese, 1 whole egg, 2 egg yolks