Place the sweet potatoes, 3 cups of chicken broth, the beer, cumin, and bay leaf in a medium saucepan. Bring to a boil, then simmer until the potatoes are crisp-tender, 12-15 minutes. Discard the bay leaf.
Meanwhile, cook the bacon until crisp in a large stockpot. Remove the bacon and drain on paper towels; when it is cool, chop or crumble it. Add the onion and garlic to the fat remaining in the pot; saute over medium-high heat until quite soft, about 10 minutes. Add the sweet potatoes with the cooking liquid to the onion and stir in the remaining 3 cups broth as well.
Add the creamed corn and green chiles to the soup and season with the chili powder and cayenne. Gradually stir in the milk and cream. Simmer the soup, uncovered, for 10 minutes.
Shred 12 ounces of the cheese and cut the remaining 4 ounces into small dice. Reduce the heat under the soup to low and add the shredded cheese, stirring just until melted. Season the soup with salt and stir in the cilantro. Ladle into bowls, stirring a tablespoon of diced cheese into each.