Heat olive oil in a large skillet or pot.
Add onions and red pepper, cook and stir until tender.
Add garlic, cook and stir until fragrant.
Stir in chicken broth and ham.
Taste broth and season with salt and pepper as needed.
Add turnip greens and allow them to cook down slightly.
Reduce heat to medium-low and simmer for 15 minutes or longer, to taste. Stir every 15 minutes.
Add cider vinegar and hot sauce, if using. Stir until incorporated.