Preheat the oven to 375°F (190°C) with a rack in the center position.
Wash and dry the squash, cut the ends off, then slice thinly into rounds.
Carefully unfold the puff pastry sheet on a small baking sheet lined with parchment paper or a Silpat mat.
With a sharp knife, score the pastry about ½ inch from the edges to create a border being careful not to cut all the way through.
Spread the pesto evenly on the crust inside the border. Arrange the squash slices on the crust overlapping a bit, creating any pattern you like. Sprinkle over salt, pepper, and parmesan cheese. Drizzle with olive oil.
Bake for 20-22 minutes, or until the crust is puffed up and golden brown. Cool on a wire rack for 3 minutes before cutting into squares. Serve warm or at room temperature.