Preheat your oven to the temperature recommended on the puff pastry package instructions (usually around 400°F or 200°C). Line a baking sheet with parchment paper.
In a small bowl, combine the softened butter with minced garlic, chopped fresh parsley and grated Parmesan cheese. Mix well to create the garlic and herb mixture.
Unfold the thawed puff pastry sheet onto a lightly floured surface. Roll it out slightly to even out the creases and make it slightly thinner. Brush the entire surface of the puff pastry sheet with the butter mixture, covering it evenly.
Starting from one edge, tightly roll up the puff pastry sheet, creating a log or roll.
Using a sharp knife, slice the rolled puff pastry into rounds, about 1/2 to 3/4 inch thick. Place the sliced rounds onto the prepared baking sheet, leaving a bit of space between each one. Bake the puff pastry swirls in the preheated oven for about 12-15 minutes, or until they are golden brown and puffed up.
Once baked, remove the swirls from the oven and let them cool slightly on the baking sheet before transferring them to a wire rack to cool completely. Serve the garlic and herb puff pastry swirls as a delightful appetizer or snack. They can be enjoyed warm or at room temperature.