Remove the thick fibrous outer leaves from the cabbage, cut it into quarters and wash it.
Finely slice the cabbage and the apples (about ¼-inch thick).
In a large bowl place cabbage, sliced apples, half of the crumbled cheddar, and half of the walnuts (reserve the rest for the topping).
In a small bowl or in a glass, make a vinaigrette mixing extra virgin olive oil, vinegar, salt (I start with ½ tsp) and a good pinch of black pepper. Pour the dressing over the salad, toss well, taste and adjust the seasoning according to your taste.
Serve at room temperature with chopped walnuts and crumbled cheddar on top. Enjoy.
