Thaw the puff pastry until it unfolds easily but remains cool and slightly firm.
Preheat the air fryer to 350°F for about 3 minutes if your model allows preheating.
While your air fryer preheats, lightly flour your work surface if the pastry feels sticky.
Unfold the thawed puff pastry sheet. Gently press out any major creases with your fingers or a rolling pin, but do not roll it too thin.
Using a sharp knife or a pizza cutter, cut the pastry into roughly 1x2 inch rectangles. They do not need to be perfect.
Spread the rectangles in a single layer in the basket of your air fryer, leaving a little space between each one so they can puff.
Air fry at 350°F for 6 to 9 minutes. Pause around minute 4 or 5 to gently shake the basket or flip the bites for even browning.
Remove when puffed, crisp, and golden.
Make the cinnamon sugar. In a shallow bowl, stir together the granulated sugar and ground cinnamon.
While still warm, brush each churro bite with melted butter (front and back). Then, toss the warm churros in the cinnamon sugar mixture until well coated.
Pile the churro bites on a plate or in a shallow bowl. Serve with small bowls of chocolate sauce or caramel sauce for dipping.