Cook in a large skillet over medium heat until browned on all sides, about 20 minutes. Stir in cream of mushroom soup, 2 1/2 cups milk, salt, and pepper. Cover and simmer, stirring occasionally, until thickened to gravy consistency, at least 1 hour.
Place potatoes into a large pot and cover with water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain. Add 1/4 cup butter, 1/4 cup milk, salt, and pepper; beat with an electric mixer until smooth.
Heat corn in a saucepan over medium heat until tender, about 15 minutes. Season with salt and pepper.
Pour beef and gravy mixture over mashed potatoes and place corn on the side to serve.