First things first, preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper. Lightly flour your work surface and carefully unroll your thawed puff pastry sheet on top. If the pastry feels too soft or sticky, pop it back in the fridge for 10 minutes to firm up.
Now for the fun part. Using the back of a spoon or a spatula, spread the pesto evenly over the entire surface of the puff pastry, leaving a tiny border along one long edge. This will help seal the roll. Next, sprinkle the chopped sun-dried tomatoes and the freshly grated Parmesan cheese evenly over the pesto.
Starting from the long edge opposite the clean border, tightly roll the pastry into a log. Use a sharp knife to slice the log into 1-inch thick rounds. Place each pinwheel flat on the prepared baking sheet, leaving some space between them. Brush the tops and sides with the beaten egg and bake for 15-20 minutes, or until puffed and golden brown.