Rinse cabbage under cold water and place damp cabbage in a Dutch oven with apple, apple juice, cup water and vinegar. Cover and heat over medium heat for 15 minutes. Reduce heat to low and cook about 35 to 40 more minutes, until cabbage is tender and apple pieces are mushy, stirring occasionally. Add water by the cup when the cabbage gets dry, about every ten to 15 minutes. When tender, uncover and raise heat to medium high. Cook, stirring until liquid is evaporated. Season with salt and stir in goat cheese until evenly distributed. Serve warm.