Prepare the cabbage: After coring and shredding the cabbage, rinse it under cold water and drain well. You want the shreds to be separate and not clumped together. The sound of the crisp shreds hitting the colander is a good sign you've cut them thinly enough.

Sauté the aromatics: Heat the olive oil or butter in a large, heavy-bottomed frying pan or Dutch oven over a medium heat. Add the sliced onion and cook for 5-7 minutes, stirring occasionally, until it becomes translucent and fragrant. You'll notice the onion releasing a gentle, sweet aroma.

Add the garlic and apples: Stir in the minced garlic and diced apples. Cook for another 2 minutes until the garlic is fragrant but not browned. The apples should begin to soften slightly at the edges.

Combine the cabbage: Add the shredded red cabbage to the pan. It will look like a mountain, but don't worry. Toss it with the onion and apple mixture using a wooden spoon. Cook for 3-4 minutes, stirring frequently. You'll see the cabbage begin to wilt and turn a deeper, richer shade of burgundy.

Add the liquids and seasonings: Pour in the apple cider vinegar, stock, brown sugar or honey, caraway seeds (if using), salt, and pepper. Stir everything together until the sugar dissolves. The liquid should be bubbling gently around the edges of the pan.

Simmer until tender: Reduce the heat to low, cover the pan with a lid, and let it simmer for 35-40 minutes. Stir occasionally. The cabbage will release more liquid as it cooks. You'll know it's done when the shreds are tender but still hold their shape, and the liquid has reduced to a thick, syrupy glaze that clings to the cabbage. The smell will be wonderfully sweet and tangy.

Finish and glaze: Remove the lid, increase the heat to medium-high, and add the balsamic vinegar. Cook for 2-3 minutes, stirring constantly, until the remaining liquid has reduced to a glossy coating. The cabbage should be shiny and no liquid should pool in the bottom of the pan.

Rest and serve: Remove from the heat and let it stand for 5 minutes. This allows the flavours to meld. Taste and adjust seasoning with salt and pepper if needed. Transfer to a serving dish and garnish with fresh parsley or chives.