In the bowl of a slow cooker, combine the beer, 3 cups water, the chilies, adobo sauce, cumin, onion, beans, pork, and 1 1/2 teaspoons salt. Set the slow cooker to high and cook, covered, until the beans are tender and the pork pulls apart easily, 4 to 5 1/2 hours. Using a fork, separate the pork into large pieces. Divide among individual bowls and top with the sour cream, salsa, and cilantro.
If You Don't Have a Slow Cooker: Heat oven to 300° F. Follow the recipe above using a Dutch oven or large casserole. Bake, covered, until the pork pulls apart easily, 4 hours.