Set aside half an onion and chop the rest. Heat the olive oil in a large skillet over medium-high heat. Add the chopped onions, carrots and garlic; sprinkle with the flour and cook, stirring, until slightly browned, 5 minutes. Add 2 tablespoons water and scrape up any browned bits from the pan. Transfer the vegetables and cooking liquid to a slow cooker. Add the beans, turkey drumstick, pickling-spice packet, red pepper flakes and 8 cups water. Cover and cook on low 6 hours.
Remove the drumstick and shred the meat; keep warm. Remove about 2 cups beans from the cooker and blend until smooth (or partially blend with an immersion blender). Return the beans and turkey meat to the soup. Season with salt and pepper.
Mince the reserved 1/2 onion. Ladle the soup into bowls and top with the cilantro and minced onion. Garnish with sour cream and lime, if desired.