Heat olive oil in a large pot over medium heat.
Add chopped onion and cook until soft, about 3–4 minutes.
Stir in garlic and cook for 1 minute until fragrant.
Add smoked turkey and pour in the chicken broth. Bring to a boil.
Add collard greens, pressing them down as they wilt.
Season with salt, pepper, and red pepper flakes.
Reduce heat to low, cover, and simmer for 1–1.5 hours until greens are tender.
Stir occasionally and add more broth if needed.
Finish with apple cider vinegar, taste, and adjust seasoning before serving.