Peel and grate the potato. Place pieces in a bowl of cold water.

Peel and ice the onions.

Melt the butter in a skillet over medium heat.

Add the onions, stir to coat, and fry until transparent.

Remove from stove and set aside.

Peel and core the green apples. Chop into small pieces.

Place a cabbage layer on the bottom of a Dutch oven.

Cover the cabbage with a layer of the green apple pieces.

Repeat this process, ending with a layer of cabbage on top.

Sprinkle the white vinegar over the top.

Whisk together the sugar, salt, and freshly ground pepper.

Sprinkle the mixture evenly over the cabbage in the saucepan.

Gently pour the 2 cups of hot water over the cabbage and apples.

Cover the saucepan and bring everything to a boil over medium-high heat.

Reduce the heat to low. Simmer for 30 minutes or until the cabbage is tender.

Drain the grated potato and combine with the caramelized onions.

Mix into the cabbage.

Simmer for 10-15 minutes.

Serve immediately.