Prepare the oven: Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
Roll the pastry: On a lightly floured surface, gently roll the cold puff pastry into an even rectangle.
Add the filling: Spread the pizza sauce over the pastry, leaving a small border along one long edge. Sprinkle evenly with shredded cheese and oregano.
Roll into a log: Starting from the opposite long edge, roll the pastry into a snug log without squeezing out the filling. Gently press the seam to seal.
Slice: Using a sharp knife, cut into 14 rounds, approximately ¾ inch (2 cm) thick. If the pastry becomes too soft to slice cleanly, refrigerate it briefly first.
Bake: Arrange the rolls cut-side up on the prepared baking sheet, leaving space between them. Bake for about 10 minutes, or until puffed, lightly golden, and cooked through. Continue baking as needed if the centers are still underbaked.
Serve: Allow to cool for a few minutes, then serve warm with extra pizza sauce for dipping, if desired.