1. Remove the puff pastry from the refrigerator and let it sit at room temperature until it is easy to unroll.

2. Preheat the oven to 400°F. Line 2 baking sheets with parchment paper.

3. In a medium bowl, combine the softened butter, minced garlic, parsley, salt, and black pepper. Mix until well blended.

4. Unroll the puff pastry onto a clean work surface.

5. Spread the garlic butter mixture evenly across the entire surface of the pastry.

6. Sprinkle the shredded cheese evenly over the garlic butter layer.

7. Starting from one of the long sides, tightly roll the pastry into a log. Place it seam-side down.

8. Slice the log into 1-inch pinwheels and arrange them on the prepared baking sheets, leaving space between each piece.

9. Brush the tops and sides of the pinwheels with the beaten egg.

10. Bake for 15 minutes, or until the pastry is puffed and golden brown.

11. Allow the pinwheels to cool for a few minutes before serving. Serve warm.