Combine chicken broth, chicken breast cubes, onion, carrots, celery, bay leaf, salt, and pepper in a large pot; bring to a boil. Reduce heat, cover pot, and simmer until chicken is no longer pink in the center and the vegetables are tender, 20 to 25 minutes.
Mix baking mix and milk in a bowl until dough is sticky; drop golf ball-sized pieces of dough into the soup. Cover pot and cook until dumplings are cooked through, about 10 minutes.
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