Clean the Savoy cabbage and discard the tough outer leaves and hard ribs. Wash the remaining leaves thoroughly and cut them into thin strips.
In a large skillet or pan, heat the olive oil and lightly sauté the garlic clove until fragrant.
Add the cabbage strips and cook for about 10 minutes to soften. If the cabbage appears too dry during cooking, add a small splash of warm water.
Pour in the white wine and let it evaporate over medium heat. Dilute the tomato paste in a small amount of warm water, then stir it into the cabbage. Season with salt and black pepper to taste.
Continue cooking the cabbage over low heat for approximately 60 minutes, stirring occasionally and adding a little warm water if necessary to prevent sticking.
About 5 minutes before the end of cooking, prepare the sweet-and-sour mixture by thoroughly dissolving the sugar into the cider vinegar in a small bowl.
Pour the sweet-and-sour mixture over the cabbage, toss well to coat, and let the flavors meld for the final few minutes of cooking before serving.