Step 1

Place oil and turkey tail in a large saucepan. Set over medium heat and cook, turning occasionally, until brown on all sides, about 5 minutes. Add onion; cook, stirring occasionally, until starting to take on some color, about 4 minutes. Add bell pepper; cook, stirring, 1 minute. Add garlic, hot sauce, peperoncini, brine, thyme, and beans, then pour in broth. Bring to a boil; reduce heat and simmer, skimming any foam from surface, until beans are tender and liquid thickens slightly, about 2 hours. Shred meat on tail and mix into beans; discard tail.

Step 2

Do ahead: Beans can be made 3 days ahead. Chill in an airtight container.