Put the ham in a large stockpot over medium heat. Cook until the ham is crispy and the fat is rendered, about 8 minutes. Pour in the apple cider vinegar and scrape the bottom of the pot with a wooden spoon to lift up any brown bits.
Meanwhile, rip the greens into large pieces to make it easier to fit all of them into the stockpot.
Add the greens to the pot and season generously with black pepper. Pour in the chicken stock and stir to combine. Bring the greens to a simmer and cover the pot. Reduce the heat to medium low and cook until the greens are tender and the liquid is reduced by half, about 45 minutes. Remove the lid and continue to cook, stirring occasionally, until the liquid is nearly gone, about 10 minutes more. Serve immediately.
If you cannot find country ham, use good-quality smoked ham with lots of fat. The 1 pound of greens is weighed after the stems are removed. It is about 25 cups of greens.