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Step 1
Preheat oven to 375°F. Line a 10x15-inch jelly roll pan with parchment paper and grease with cooking spray. Cut a second piece of parchment paper the same size and set aside.
Step 2
In a medium bowl, combine flour, pumpkin pie spice, baking powder, baking soda, and 1/4 tsp. salt. In a second bowl, whisk together brown sugar, pumpkin puree, eggs, melted butter, and 1 tsp. vanilla. Add dry ingredients to the pumpkin mixture and whisk just until no streaks of flour remain.
Step 3
Pour cake batter into the prepared pan and spread it into an even layer all the way out to the edges so it bakes evenly.
Step 4
Bake until the cake appears dry, starts to pull away from the edges of the pan, and springs back when pressed, 10-12 minutes.
Step 5
As soon as the cake comes out of the oven, run a metal spatula or thin knife around the edges of the cake and carefully slide it out on the parchment paper onto a clean surface. Spray the second sheet of parchment paper with nonstick spray and place it spray side-down on top of the cake. Place a clean kitchen towel on top of the parchment paper, which will keep the cake from rolling up too tightly and cracking. Start with one short end and carefully roll the hot cake into a log (use a second towel to protect your hands, if needed). The cake will resist at first, but it will get easier as you roll.
Step 6
Let the cake cool on a wire rack until room temperature, about 1 hour.
Step 7
Meanwhile, prepare cream cheese frosting. Add cream cheese, room temperature butter, powdered sugar, and remaining 1 tsp. vanilla extract and 1/4 tsp. salt to the bowl of a stand mixer fitted with a paddle attachment, or to a mixing bowl. Beat on low until combined, then increase speed to medium-high and beat until light and fluffy, 3-4 minutes, pausing once to scrape down the bowl.
Step 8
When the pumpkin cake has cooled, carefully unroll it and remove the towel and top parchment paper. The parchment may stick slightly; use a spatula as needed to carefully peel it off of the cake. Top the unrolled cake with the frosting and spread it out in an even layer, leaving a 1/2-inch border around all of the sides.
Step 9
Starting with the same short end, carefully roll the cake back up into a log, removing the bottom parchment paper from the cake as you go. Once the cake has been rolled up completely, cover tightly with plastic wrap and chill in the fridge for at least 2 hours to firm up the frosting and up to 2 days ahead.
Step 10
Just before serving, remove plastic wrap and dust cake with powdered sugar, then cut cake into slices. Serve slices topped with chopped candied pecans if you like.