Preheat the oven to 350°F. Spray a 9x13 inch pan with cooking spray. Set aside.
In a medium skillet, brown the ground beef and onion. Drain and set aside.
Meanwhile, in a medium saucepan, melt the butter over medium low heat. Stir in the cornstarch. Slowly add the beef broth and milk, mixing until smooth. Bring to a gentle boil, cooking until thickened.
Remove from heat and add in the cream of mushroom soup and water.
Layer the bottom of the prepared dish with half of the hashbrowns, then half of the soup mixture, then half of the ground beef mixture. Repeat with the remaining potatoes, soup mixture and ground beef.
Sprinkle the cheese over the mixture. Cover with foil and cook in the preheated oven for 45-60 minutes. Remove foil and cook uncovered for an additional 5 minutes.