Chop your onion.
Cook the onions and ground beef in a large soup pot until browned.
Add your beef stock and flour (wait on the arrowroot until the end if you're using that).
Chop all the other veggies and add them, too.
Add the mustard powder, salt, and pepper.
Allow this to cook on low-medium heat for about an hour until all the veggies are tender.
Add the milk and the cheese. (If you're using arrowroot, mix the cold milk with the arrowroot before adding it.)
If you want it thicker, add a little more flour or arrowroot mixture.