In a large soup pot on medium heat, add onion and ground beef. Cook for about 5 minutes, until beef is browned and onion is soft.
Add garlic, chicken stock, mustard powder, and potatoes; simmer for 10 - 15 minutes, or until potatoes are tender.
Add broccoli, and cook for only 3 - 4 minutes. The broccoli should still be bright green and tender.
Mix milk and arrowroot powder; pour into hot soup and stir until thickened.
Add cheese and salt (start with about 1 tsp, less if using boxed stock with salt already added) and stir until smooth. Taste and adjust salt if needed.