Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Dust a flat work surface lightly with flour. Unroll puff pastry sheet and roll out into a rectangle. Spread pesto evenly over puff pastry, smoothing it out with a spoon. Scatter pine nuts evenly over the pesto and top with grated Parmesan cheese.
Roll puff pastry up tightly like a jelly roll from the longer side. Brush with milk to glaze.
Slice puff pastry roll into 12 to 15 pinwheels about 1/2-inch-thick. Lay pinwheels on the prepared baking sheet, leaving some space between each one.
Bake in the preheated oven until pastry is lightly browned, 15 to 20 minutes. Let sit for 1 minute on baking sheet before removing.