Cook and stir bacon and ham together in a large pot over medium-high heat until some of the bacon fat renders, 7 to 10 minutes. Add the onion and continue cooking until the bacon and ham are browned and the onion translucent, 5 to 7 minutes more.
Pour milk and potato soup into the pot; add potatoes, garlic salt, and pepper. Reduce heat to medium-low and cook mixture at a simmer, stirring frequently, until heated through and slightly thickened, about 20 minutes.
Ladle soup into bowls and top with Cheddar cheese and green onions.