Use a food processor to finely mince the onion, garlic, and bell pepper.
In a very large pot (at least 5 qts), heat the olive oil over a medium heat and then sautee the minced onion and pepper mixture with a good pinch of salt and pepper until the mixture is soft - about 3-5 minutes.
While that cooks, use the grating attachment of your food processor to grate the sweet potatoes. If you are not using a food processor, then finely chop the sweet potatoes as small as you like. It will be totally fine if it is chunkier. It will just take the sweet potato longer to soften in the soup.
Chop of the stems of cilantro and add to the soup. Save the leaves for serving.
Add the chopped up chicken, and spices with another pinch of salt.
Pour in the can of diced tomatoes, liquid and all. Then add the chicken broth. Stir and then add the rinsed cans of black beans and red kidney beans. Bring it to a simmer and put the lid on for about 30 minutes. It can simmer for much longer if you need to leave it for a bit. Stir occasionally to make sure nothing is sticking to the bottom. Check the seasoning to make sure there is enough salt and pepper to your taste. Add more as needed.
Add the frozen corn and cream. Bring it back to a simmer for another 10 minutes or so.
Just before serving add a several tablespoons of fresh cilantro and chopped green onions.
Serve with optional toppings such as: tortilla chips, fresh cilantro, hot sauce, chopped green onions, sour cream, shredded cheese, lime wedges, and avocado.