Remove the stem from the rehydrated chile pepper. Combine with 1 can of chicken broth in a blender or food processor, and puree until smooth. Pour into a 5 or 6 quart slow cooker.
Pour in the remaining can of chicken broth, and add the beef broth, pork, chicken, onion, garlic, green chilies, and white and yellow hominy. Season with the bay leaf, oregano, and cumin. Cover, and cook on High for 4 to 5 hours, or on Low for 6 to 7 hours. Remove the bay leaf before serving.