Heat the oil in a large Dutch oven over medium heat. When the oil is hot, add the onions and cook until softened, 3 to 4 minutes. Stir in the garlic and cook until fragrant, another 2 minutes. Add half of the mustard greens, season with salt and pepper, and cook, stirring, until the greens are wilted and reduced in volume by half, about 5 minutes. Add the remaining greens and season with more salt and pepper; cook again until the greens are wilted and evenly incorporated with the onions and garlic.
Add the chicken stock, vinegar and ham hock to the pot and bring to a boil. Turn the heat to low, cover, and cook at a slow simmer for 1 1/2 hours, stirring halfway through. The greens are done when the stock has almost completely reduced and the ham hocks are tender when pierced with a pairing knife.
Remove the ham hocks to a cutting board and pull the meat from the bone with two forks. Discard any fat and skin, and then stir the shredded meat back into the greens. Season with salt and pepper to taste. Serve immediately.