Place the shredded cabbage in a large, heat-proof mixing bowl. In a medium saucepan, combine the vinegar, sugar, pickling spice, 2 teaspoons salt and 1 1/2 cups water. Bring to a boil, stirring to dissolve the sugar and salt, then pour the mixture over the cabbage. Set a plate on top of the cabbage to weight it down. Refrigerate and leave to pickle for 4 hours.
Preheat a grill or grill pan to high. Quarter the apples and cut out the cores. Toss the apples in a bowl with the lemon juice and olive oil and season with salt and pepper. Grill the apples for 1 minute on each side to achieve nice grill marks. Set the apples aside to cool, then cut them into dice.
When the cabbage is ready, drain it well and return it to the bowl. Fold in the grilled apples and serve.
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