Heat oven to 400° F.
Cut the puff pastry into 4 squares. Line 4 rounds of a muffin tin with the squares, allowing the corners to stick out.
In a small bowl, combine the apple, sugar, and walnuts. Fill each pastry square with some of the mixture and bake until the crusts are golden brown, about 25 minutes. Let cool 10 minutes before removing from the tin.
Place one tart on each plate. Serve with the whipped cream, if desired.