Preheat your oven to 375°F (190°C). Line a 17-inch baking sheet with parchment paper and lightly coat it with non-stick spray.
Prepare a large cutting board with another piece of parchment paper, and set it aside for later use.
In a medium mixing bowl, whisk together the flour, baking powder, baking soda, pumpkin pie spice, and salt until well combined.
In a separate large bowl, beat the eggs, sugar, and vanilla extract with an electric mixer on high speed until the mixture is thick and pale. Fold in the pumpkin puree until fully integrated.
Gradually incorporate the dry ingredients into the wet mixture, stirring until just combined.
Spread the batter evenly onto the prepared baking sheet, smoothing the top with a spatula. Bake for 13-15 minutes, or until the cake springs back when lightly pressed in the center.
Once removed from the oven, promptly invert the cake onto the prepared cutting board with parchment paper. Carefully peel away the parchment that was baked with the cake.
While the cake is still warm, gently roll it up with the parchment paper, starting from the short side. Let the rolled cake cool completely on a wire rack, approximately 2 hours.