Chop the tough ends of the stems off of each bunch of turnip greens. Chop each bunch of greens by bundling them together with one hand and chopping into about 1-inch sections. Transfer chopped greens to the basin of a clean, large, deep sink.
Cover greens with water and with both hands, rub and toss greens in water to remove dirt and grit. Drain water and repeat process 3-5 times until greens are clean and no dirt is evident in water.
Heat oil in a large stock pot or dutch oven over medium high heat. Add onion and chopped turnip roots and cook for 3-5 minutes. Add garlic and saute until fragrant.
Add greens in two batches, stirring with a wooden spoon after each addition to wilt greens. After all greens have been added, pour in stock and stir to incorporate. Bring greens to a boil.
Once greens come to a boil, reduce heat to medium and add spices, brown sugar, liquid smoke and vinegar. Stir to incorporate all ingredients. Cover pot and simmer for 45 minutes, stirring occasionally.
Remove the lid after 45 minutes and continue to cook greens for about 15 minutes longer. Add more salt and pepper to taste if desired. Once greens have reached your preferred level of tenderness, transfer them to a serving bowl with some of the cooking liquid. Enjoy!