Sauté aromatics: Heat olive oil in a large pot over medium heat. Add onion and cook until soft, about 3–4 minutes. Stir in garlic and cook 1 minute more.

Brown the meat (if using): Add smoked sausage or ham hock and cook for 2–3 minutes.

Add greens and broth: Stir in chopped turnip greens (and roots if using). Pour in broth, scraping up any browned bits.

Add beans: Mix in drained beans. Bring soup to a simmer.

Simmer: Cook uncovered for 25–30 minutes, stirring occasionally, until greens are tender.

Season and finish: Add salt, pepper, and red pepper flakes. Before serving, stir in vinegar or lemon juice for brightness.

Serve: Ladle into bowls, add desired toppings, and enjoy!