Preheat the oven to 400 degrees. Lay the puff pastry sheets on a work surface. Place half of the walnuts and chopped apple in the center of each. Place a cheese wheel on top, then trim the corners of each pastry sheet to make a disk. Brush the edges lightly with water and fold up and over to cover the cheese; pinch lightly to seal. Place seam side down on a parchment-paper-lined baking sheet and bake until golden-brown, 30 to 35 minutes.
Transfer each cheese pastry to a platter and let cool for 10 minutes; serve with the sliced apples.