In a Dutch oven, heat oil over medium-high heat. Add onion; cook and stir until tender, 6-8 minutes. Add garlic; cook 1 minute longer. Stir in broth, tomatillos, tomatoes and red pepper. Bring to a boil; reduce heat. Simmer, covered, until vegetables are tender, about 15 minutes. Cool slightly and puree in batches in a blender.
Place chicken in a 5- or 6-qt. slow cooker; sprinkle with taco seasoning. Pour pureed tomatillo mixture over top. Add garbanzo beans and black beans. Cook, covered, on low until a thermometer inserted in chicken reads 165°, 3-1/2 – 4 hours.
Remove chicken; shred with 2 forks. Return to slow cooker. Add corn. Cook, covered, until heated through, 15-30 minutes longer. Serve with toppings of your choice. Freeze option: Freeze cooled soup in freezer containers. To use, partially thaw in refrigerator overnight. Heat through in a saucepan, stirring occasionally and adding a little broth if necessary.