Heat a large pot or Dutch oven over medium-high heat. Cook and stir beef until browned and crumbly, 5 to 7 minutes; drain and discard grease. Add diced potatoes and onion; cook and stir until onion is tender, 5 to 10 minutes.
Mix milk, processed cheese food, and Cheddar cheese into beef mixture; bring to a boil. Reduce heat and simmer, stirring often, until heated through and cheese is melted, 15 to 20 minutes; season with pepper. Add mashed potatoes for a thicker chowder; cook until heated through and thickened, about 5 minutes.