For Soup: Heat olive oil in a large pot over medium-high heat. Add onion and sauté until translucent, about 5-7 minutes. Add garlic and saute for an additional 30 seconds to 1 minute. Stir in chicken, tomatoes, beans and corn. Add broth, Stubb's Sweet Heat Bar-B-Q Sauce, Stubb's Bar-B-Q Spice Rub, salt and black pepper; stir to combine.
Bring soup to a boil. Boil for 4-5 minutes, then reduce heat to low and simmer for 10-15 minutes. Taste and adjust seasonings, if needed. Serve topped with cornbread croutons.
For Croutons: Preheat oven to 400° degrees F. Place cornbread on a large baking sheet. Bake cornbread croutons in preheated oven for 12-15 minutes, or until golden brown and crispy.