Place soups, chicken broth, salt, and garlic seasoning into a crock-pot over low heat. Whisk until smooth. Place chicken in, pressing to the bottom. Cover lid and cook on low for 6 hours or on high for 3 hours.
When chicken is cooked, use 2 forks to shred into bite size pieces. Stir in sour cream and broccoli.
Serve over steamed rice and sprinkle with cheese.