Preheat the oven to 375°F and line a baking sheet with parchment paper. Thaw the puff pastry according to package directions.
Place the apples on their sides on a cutting board and slice into ¼-inch thick rounds, making 8 to 10 slices. Use a small cookie cutter or the lid of a pop bottle to punch out the cores, creating donut shapes.
On a lightly floured surface, roll out the puff pastry and slice into 8 long, even strips. Wrap each strip around an apple ring, slightly overlapping as you go, until fully covered. Place the wrapped rings onto the prepared baking sheet.
In a small bowl, mix together the sugar and cinnamon. Lightly brush both sides of each donut with oil, then generously sprinkle with the cinnamon sugar mixture.
Bake for 25 to 30 minutes, until the pastry is golden brown and crisp. Allow to cool slightly before serving. These are best enjoyed immediately!