Brown the ground beef along with the chopped onion in a large skillet over medium heat until the beef is nicely browned and the onion is tender.

Add the sliced carrots, celery, and frozen peas to the skillet. Cook together until the veggies start to soften, about 5 minutes.

Stir in the cooked egg noodles, cream of mushroom soup, milk, and half of the shredded cheddar cheese. Mix until creamy.

Transfer the mixture into a greased 9x13-inch baking dish and sprinkle the remaining cheese on top.

Bake in a preheated oven at 350°F for 25 to 30 minutes, or until bubbly and golden brown.