Preheat oven to 375°F (190°C). In a large skillet, brown the ground beef and chopped onion over medium heat until cooked through. Drain any excess grease.

In a large bowl, combine the cooked beef and onion mixture with the cream of mushroom soup, milk, cooked egg noodles, salt, and pepper. Mix well to ensure all ingredients are evenly distributed.

Transfer the mixture into a 9x13 inch baking dish. Sprinkle the shredded cheddar cheese evenly over the top of the casserole.

Bake for 25-30 minutes, or until the casserole is bubbly and the cheese is melted and lightly golden brown. Let stand for a few minutes before serving.