In a large pot, brown the ground beef over medium-high heat until fully cooked. Drain most of the excess grease, leaving about 1 tablespoon in the pot.
Add diced onions, carrots, celery, onion powder, and garlic powder to the pot with the beef. Cook for 3 minutes. If it begins to stick, deglaze the pot with a splash of the broth.
Add diced potatoes, ketchup, mustard, and beef broth to the pot. Bring to a boil, then reduce heat and simmer until potatoes are tender, about 15 minutes.
Reduce heat to low. Stir in milk, cheddar cheese, Velveeta, and sour cream. Cook until cheese is melted and the chowder is heated through. Season with salt and pepper to taste.