Cook the Ground BeefHeat a large pot or Dutch oven over medium heat Add the ground beef and cook until browned, breaking it apart with a spoon.
Drain excess fat and set the beef aside.
Sauté the VegetablesIn the same pot, melt 2 tablespoons of butter over medium heat. Add the onions, carrots, and celery, and sauté for about 5 minutes until softened.
Add the diced potatoes, chicken broth, garlic powder, and paprika.
Simmer the Soup BaseBring the mixture to a boil, then reduce the heat to a simmer. Cover and let cook for 10-15 minutes, or until the potatoes are tender.
Create the Cheese SauceIn a medium bowl, melt the remaining 1 tablespoon of butter. Whisk in the flour to form a roux. Cook for 1 minute, stirring constantly.
Gradually whisk in the milk until smooth. Cook until thickened, about 3-4 minutes.Stir in the shredded cheddar cheese until melted.
Combine and FinishPour the cheese sauce into the soup pot. Add the cooked ground beef and stir to combine.
Reduce the heat to low and stir in the sour cream.
Taste and season with salt and pepper as needed.
Serve and GarnishLadle the soup into bowls. Top with optional garnishes like crumbled bacon or extra cheese.