Trim the cabbage, removing and discarding the tough outer leaves. Separate the remaining leaves, rinse them thoroughly, and slice them into thin shreds. Peel and crush the garlic clove.
Heat the olive oil in a large saucepan or pot, then add the shredded cabbage and the crushed garlic.
Season with salt and cook for about 10 minutes, allowing the cabbage to soften.
Pour in the white wine and let it partially evaporate over medium heat. Dilute the tomato paste in 200 ml (approx. 2 dl) of lukewarm water, add it to the pan, and stir well to combine the flavors.
Cover the pot with a lid and continue braising over very low heat for about 1 hour, stirring occasionally with a wooden spoon.