Put ground beef in a soup pot and brown. Drain the fat, and set aside beef.
Dice the garlic, onions, carrots, and celery. Add to the pot you used to cook the beef. Saute 8 to 10 minutes until soft. Dice the potatoes and set aside.
Whisk in the gluten free flour, and cook for one minute. Slowly add the broth and milk and continue whisking until smooth. Sauce should be slightly thick.
Add the potatoes, bring to bubbling, turn down the heat, cover, and cook until potatoes are soft, about 20 to 30 minutes. Stir frequently.
When potatoes are soft, add beef, Daiya cheese style shreds, and salt and pepper. Stir until the cheese style shreds are melted and the soup is creamy. Serve.