Cook the Ground BeefIn a large pot or Dutch oven, cook the ground beef over medium heat until browned. Remove with a slotted spoon and set aside. Drain any excess grease.
Simmer the SoupAdd the cubed potatoes and pour in the chicken or beef broth. Bring to a boil, then reduce the heat and let it simmer for 10-15 minutes, or until the potatoes are fork-tender.
Prepare the Cheese SauceIn a separate saucepan, melt the remaining 2 tbsp of butter over medium heat. Whisk in the flour and mustard powder to form a roux. Cook for 1-2 minutes. Gradually whisk in the milk, stirring constantly until smooth and slightly thickened. Reduce heat and slowly add the shredded cheese, stirring until melted.
Combine EverythingAdd the cooked ground beef back into the pot with the vegetables. Stir in the cheese sauce. Season the soup with salt and pepper to taste. Cook for an additional 5 minutes, stirring occasionally.
Serve and GarnishLadle the soup into bowls and garnish with crumbled bacon, chopped green onions, and extra cheddar cheese.