Chop the medium onion into 1/3" pieces. Add the onion to a skillet with 1/4 cup melted butter. Saute on medium heat while stirring until the onion is a light caramel color.
In a large bowl, add the shredded potatoes, cream of mushroom soup, sour cream, one and a half cup of cheese, onions, garlic salt, and chicken broth. Stir until well mixed to assemble the casserole.