Remove stem and seeds from the persimmons, use a spoon to remove the flesh and puree it in a blender. Meanwhile, remove the puff pastry from the fridge and let it gain room temperature. Smear butter in a 15cm tart pan, place the pastry and cut the excess. Use a fork to pierce the pastry inside the pan, add the persimmon puree, salt and pepper, the pine nuts, pieces of butter for taste and moisture, and bake in the oven set to fan at 180oC for 30 minutes. Serve with arugula leaves and roasted pine nuts.