In a large skillet over medium heat, add the ground beef. Cook until browned and no longer pink, about 5-7 minutes.
Stir in the chopped onion and cook for an additional 3-4 minutes until the onion is translucent. Then, add the frozen mixed vegetables and stir until heated through, about 2-3 minutes.
In a large bowl, combine the cream of mushroom soup and milk. Stir until smooth and then add the garlic powder, salt, and pepper. Mix this into the beef and vegetable mixture, and then stir in 1 cup of shredded cheddar cheese until well combined.
Add the cooked egg noodles to the beef and vegetable mixture. Stir gently to combine.
Transfer the mixture to a greased 9x13 inch baking dish. Spread it out evenly.
In a small bowl, combine the breadcrumbs with the melted butter. Sprinkle this mixture over the casserole and top with the remaining 1 cup of shredded cheddar cheese.
Bake for 25-30 minutes, or until the cheese is bubbly and the top is golden brown.
Allow the casserole to cool for about 5 minutes before serving.