Place the onion and olive oil in a large pot and set over medium heat. Stir the onion around until it yellows, then add the garlic. Cook the garlic until it’s fragrant, but not burned—this will only take a minute or two. Add the sliced cabbage, stir to coat the cabbage with oil, and cook until it begins to wilt. Add the salt, a few grinds of pepper, and the vinegar; then stir to combine all the ingredients. Cover the pan and reduce heat to low. Cook, stirring every now and again, for at least 1.5 hours—the cabbage should be very soft and tender.

When the cabbage is done, add the stock and bring to a boil before turning the heat to a low simmer. Cook uncovered and let simmer for about 10 minutes. You want everything to heat through. If it’s too thick, add a bit more stock or water (you do want the soup to be dense though). When everything is heated through, remove from heat and stir in the butter. Taste and add more salt and pepper to taste. Serve the cabbage over rice and add toppings of your choice: I like chopped spinach, carrot ribbons, cilantro or parsley, or grated Parmigiano-Reggiano (anything to add color!).