Preheat oven to 400°F. Coat a 24-cup mini muffin tin with cooking spray.
Place cream cheese, pumpkin, brown sugar, egg, pumpkin pie spice, vanilla and salt in the bowl of a food processor; process until smooth.
Lightly flour a work surface; roll puff pastry dough into a 10-by-15-inch rectangle. Cut the dough into 24 (2½-inch) squares using a knife or pizza wheel (you’ll end up with 4 rows of 6 squares each).
Press a square of dough into each cup of the prepared muffin tin, making sure the dough goes completely up the sides. Divide the batter evenly among the cups, filling each about ¾ full (1 scant tablespoon each). Bake until the dough is lightly browned and the filling is set, 15 to 20 minutes.
Let cool in the pan on a wire rack until cool enough to handle, then remove the tarts from the pan to the rack. Let cool to room temperature. Serve at room temperature or chilled.
