Heat the oil in a large pot or dutch oven over medium heat. Add the onion and cook until starting to soften. Add the garlic and pepper flakes and saute until fragrant, about 1 minute. Add the smoked turkey tails. Fill the pot with water to just barely cover the turkey tails. Bring to a boil, then reduce heat, cover, and simmer for 45 minutes to an hour.

Taste the broth and season to taste with salt and pepper. Add the chopped greens, stir, cover and cook an additional 1-2 hours, or until greens are cooked down and tender.

Stir in the apple cider vinegar and brown sugar. Taste. Add salt, pepper, and additional brown sugar to taste. Remove the turkey tails from the pot, and take any meat off the bone and add it back to the pot. Serve hot.