1. Sauté onions and garlic in hot oil in a 7.5-qt. Dutch oven over medium-high heat 3 to 5 minutes or until tender.
2. Stir together beef soup base and 2 cups water, and add to Dutch oven. Stir in chicken and next 9 ingredients. Bring to a boil. Cover, reduce heat to low, and cook, stirring occasionally, 2 hours.
3. Uncover and shred chicken into large pieces using 2 forks. Stir in brisket and lemon juice. Cover and cook 10 minutes. Serve with hot sauce, if desired.
Note: We tested with Superior Touch Better Than Bouillon Beef Base and Muir Glen Organic Fire Roasted Crushed Tomatoes.