Heat oil over low heat in a large soup pot. Add onions and peppers; sauté 15–20 minutes, until soft.
Turn up heat to medium, add garam masala, and sauté for 2 minutes. Add garlic and ginger. Stir, and sauté for 1 minute. Add sweet potatoes, tomatoes and half of the chicken stock. Fill tomato can halfway with water, swish to remove tomato clinging to the can, and add to the pot.
Bring to a simmer, and cook on low for 30 minutes, until sweet potatoes are soft.
Add tikka masala sauce, garbanzos, remaining chicken stock, cauliflower and roasted chicken. Bring back to a simmer, and cook for 10 minutes, until cauliflower is cooked. Season with salt and pepper; serve with a dollop of yogurt for each bowl.