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1
Clean cabbage and discard tough outer layers. Slice cabbage in half lengthwise, and shred as finely as possible using either a sharp knife or a mandoline. Be sure to remove the inner core of the cabbage -- it's too tough to cut.
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2
Heat oil in a large saute pan over medium heat. Add onion and cook, stirring regularly, until golden, about 5 minutes. Add garlic. When garlic takes on some color, add cabbage. Using tongs, turn cabbage once or twice to incorporate it with the oil and onions, and cook until wilted.
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3
Add vinegar, salt, and pepper. Turn heat to lowest possible setting, cover pot, and cook at least 1.5 hours, stirring occasionally, until soft, tender, and practically melted. If at any point the cabbage looks dry or it looks like the bottom may burn, add a tablespoon of water to moisten. When cabbage is fully cooked, taste and adjust for salt, pepper, and vinegar. You want the cabbage just a very little bit tangy -- mostly sweet and soft and buttery. When cabbage is ready, transfer to a bowl and wipe out pot.
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4
Swirl a couple tablespoons of olive oil in the same pot you used to make the cabbage. Heat over medium. Add rice and use a wooden spoon to stir and evenly coat the kernels with the olive oil. When rice is hot to the touch, add 1 tablespoon red wine vinegar and 1 ladle of stock. Lower heat to medium-low and cook, stirring continuously, until stock evaporates. Add more stock and continue stirring. As you continue adding stock and stirring, the rice will emit some of its starch, which will thicken the risotto and make it silky. Around 10 minutes into cooking, add two ladles of cabbage. Stir to incorporate and continue stirring and adding stock as before. At around 13 minutes, begin tasting the risotto; adjust seasoning and add more cabbage if desired. Continue cooking, adding stock as necessary, until rice is done but ever so slightly al dente. Add some or all of remaining tablespoon red wine vinegar to add slight tang. Off the heat, add butter and parmesan cheese. Stir to incorporate and serve immediately.
