Preheat oven to 375°F (190°C). Line the bottom of a 10x15 jelly roll pan with parchment paper, spray the sides well with nonstick cooking spray, and set aside.
Spread out a clean kitchen towel and dust with the powdered sugar.
In a large mixing bowl, using a handheld mixer or a whisk, mix together the brown sugar, granulated sugar, and eggs for about 30 seconds - 1 minute or until well combined. Mix in the pumpkin puree and vanilla extract.
In a separate mixing bowl, whisk together the flour, pumpkin pie spice, baking powder, baking soda, and salt. Add the dry ingredients to the wet ingredients and mix together until just combined.
Pour the batter into the prepared pan and spread it around into one even layer. Bake at 375°F (190°C) for 12-15 minutes or until the top is set and a toothpick inserted into the center comes out clean.
Remove from the oven and immediately loosen the cake from the pan. Turn the cake onto the prepared kitchen towel and peel off the parchment paper. Carefully roll up the cake and the towel together starting at the narrow end. Place on a wire rack to cool completely (about 2 hours).