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Heat oven to 200C/fan 180C/gas 6. Snip the tops off the sausages and squeeze the meat out into a bowl. Stir through the grated apple and sage, then shape into 4 patties. Place the burgers on a baking sheet and cook for 25-30 mins or until golden and cooked through.
Meanwhile, mix the vinegar and sugar together with some seasoning. Stir to dissolve the sugar before stirring in the onion, cabbage and mustard. Leave to stand and soften while the burgers finish cooking. Place a burger in each roll and top with some pickled cabbage, serving any extra on the side.