Combine beef, sausage, and onion in a large skillet over medium heat; cook and stir until browned, about 5 minutes. Drain off grease and transfer to a large pot.
Stir broth, potatoes, carrots, garlic, parsley, basil, salt, and black pepper into the beef mixture. Simmer over low heat, covered, until potatoes are tender, about 15 minutes.
Mix milk and flour together in a small bowl. Pour into the pot. Bring back up to a simmer until chowder flavors combine, about 5 minutes. Remove from heat.
Stir processed cheese and sour cream into chowder when it is no longer boiling, to prevent curdling. Ladle into serving bowls and top each serving with some diced tomatoes.
