On a floured surface, roll out the puff pastry thinly (to about 3-4mm) and prick the surface all over with a fork. Cut out four 20-23cm/8-9in discs. Place in the fridge to rest.
Preheat the oven to 200C/400F/Gas 6.
Cut the apples thinly with a sharp knife. Remove the pastry from the fridge and place on a non-stick buttered baking tray. Lightly brush the edges of the pastry discs with melted butter and spread the membrillo in the middle of each disc. Arrange the apple slices on top.
Drizzle the apple with a little honey and scatter over the sugar and bake in the oven for 5-6 minutes, until golden brown.
Meanwhile, make the honey and walnut cream. Whip the double cream until thick, then fold in the walnuts and honey.
Remove the tarts from the oven and glaze with a little of the remaining butter. Serve with a spoonful of the walnut cream mixture and garnish with a sprig of mint.