In a heavy-bottomed pot, heat the vegetable oil. Add the ham hocks and sear on all sides. Meanwhile, prepare the collards by ripping the leaf away from the spine. Pile the greens on top of each other and cut into long strips; then cut the strips to make squares. Set aside.
When the ham hocks are lightly browned, add the onions and garlic to the pot; stir and sweat them until the onions are translucent and tender, 2 minutes. Add half of the greens and a cup of stock so the greens begin to wilt. Season with a pinch of salt (which will also help the wilting process) and stir to combine. Then, add the remaining greens and another cup of stock and cover to steam, about 2 minutes. Add 1–2 cups more stock, to just cover the greens and ham hocks. Season with more salt and pepper, reduce heat to a simmer, and cover. Cook, 1–1½ hours.
After 1–1½ hours, use tongs to remove the ham hocks to cool (they'll be falling off the bone). Add another ½ cup of stock, the cane vinegar, and the cane syrup to the greens. Stir, taste, and adjust seasoning if necessary. When the ham hocks have cooled, pull the meat off the bones, chop finely, and add back into the greens. Serve in a bowl with bits of ham hock and plenty of the "potlikker."