Preheat oven to 350°F (175°C).

In a large skillet, sauté chopped onion and green peppers until softened.

Add ground beef to the skillet and cook until lightly browned, drain any excess fat.

Stir in cream of mushroom soup, tomato soup, and water into the skillet.

Heat the mixture until it's well combined and slightly simmering.

In a 3-quart casserole dish, combine the cooked egg noodles, 1/2 cup of shredded sharp cheese, and the sauce mixture from the skillet.

Mix everything thoroughly to ensure the noodles are well coated.

Top the casserole with the remaining shredded sharp cheese.

Bake in the preheated oven for about 30 minutes, or until the cheese is melted and bubbly.

Let the casserole rest for 10 minutes before serving.