Heat a large heavy skillet over medium heat, and when it is hot, add the oil. When the oil is hot, add the onions and cook them for 2 – 3 minutes until they start to brown.
Add the cabbage and salt, and cook it for 2 – 3 more minutes. Add the apples and 1 Tbsp. of the vinegar, stir and cook, covered, for 5 minutes.
Uncover it and cook it for 15 more minutes until the cabbage is tender, stirring it occasionally, but not too often so it browns a bit on the bottom.
Stir in the cranberries and second Tbsp. of vinegar and cook it for 5 more minutes until the cabbage is very soft.