Preheat oven to 375 degrees F.
Pour 1/4 cup of melted butter into a 9 x 13 baking dish. Add hash browns. Mix soup, sour cream, milk, and green onions in a separate bowl. Pour 1/2 of the mixture over the hash browns. Sprinkle 1 cup of the grated cheese on top. Add remainder of hash browns and mixture on top. Sprinkle on the remaining cheese, then cover with crushed corn flakes. Drizzle 2 tablespoons of melted butter on top.
Bake for 55 minutes at 375 degrees F.