Rinse the turnip greens thoroughly to remove any dirt or grit.
Chop them into bite-sized pieces.
In a large pot, heat olive oil over medium heat and sauté the onion until it's soft.
Add the chopped garlic and stir for another minute.
Add the turnip greens to the pot in batches, stirring them to wilt slightly before adding more.
Season with salt and black pepper.
Once all greens are added, place the smoked ham hock into the pot.
Pour in the chicken broth.
Cover the pot and simmer on low for about two hours, until the greens are tender and the flavors have melded.