Set the oven rack to the middle position. Heat the oven to 375ºF (191ºC).
Line a 15-by 10-inch rimmed baking sheet (about 1-inch high sides) with parchment paper. Make sure that the parchment paper goes above the sides of the pan. Press the paper into the edges, folding the sides around the pan's rim, so it's flush with the bottom of the pan. Spray the bottom and sides of the parchment paper with cooking spray. Set aside.
In a medium bowl, whisk together sifted flour, pumpkin pie spice, baking powder, baking soda, and salt.
In a large bowl, whisk together granulated sugar, brown sugar, and eggs until light, pale in color, and smooth about 2 minutes. Add pumpkin puree, whisk until combined.
Fold the flour mixture into the pumpkin mixture, stir until no flour streaks or lumps remain. Do not overmix.
Evenly spread the pumpkin cake batter into the greased parchment paper-lined baking sheet. Make sure the batter is sitting flat in the pan. If the paper is lifted up on the edges, the cake won’t bake evenly in thickness.
Bake until the center of the cake is firm and springs back when lightly touched, about 13 to 15 minutes.
Immediately remove the cake from the baking sheet using the edges of the parchment paper. With the cake still hot, starting from the shorter 10-inch side of the cake, roll the cake with the parchment paper still attached, into a tight log.
Place the cake seam side down on a wire rack and cool completely, about 1 hour. If needed, wrap another piece of parchment paper around the roll to keep it from unrolling.
Cream Cheese Filling (makes about 1 ½ cups)
In a stand mixer fitted with a paddle, beat softened cream cheese, butter, powdered sugar, and vanilla on low speed until just incorporated. Gradually increase the speed to medium, beating the mixture until smooth 30 to 45 seconds.
Cover and refrigerate the filling until ready to assemble the cake. The filling should be cool and spreadable so that it stays thick when rolled, about 60 to 65ºF (15 to 18ºC).
Carefully unroll the cake onto a flat surface. It’s okay if the ends are slightly curled. Use a knife or offset spatula to gently separate the edges of the cake from the parchment paper. This will make it easier to roll.
The cream cheese filling should be cool but spreadable. Evenly spread the filling over the cake, leaving a 1-inch border around the edges.
Starting from the 10-inch long edge, roll the cake into a log, gradually removing the parchment paper as it’s rolled. The parchment paper will help lift and roll the cake over itself. When at the end of the cake roll, remove some of the cream cheese as needed to not overflow past the edge, for a clean seam.
Wrap the cake tightly in plastic wrap, store seam side down, and transfer to a sheet pan and refrigerate for at least 1 hour or up to 2 days. This will help set the frosting for easier slicing. The roll can also be frozen for quicker chilling.
Trim the ends off of the cake for more uniform slices, about 1/2-inch. Dust with powdered sugar and cut into even-sized pieces, about 1-inch slices.
Make your own pumpkin spice blend: 1 teaspoon cinnamon, ½ teaspoon ground ginger, ⅛ teaspoon nutmeg, ⅛ teaspoon allspice, ⅛ teaspoon cloves, ⅛ teaspoon cardamom (optional).
Room temperature eggs: Add refrigerated eggs to a bowl and cover in warm water for 5 to 10 minutes, or until they no longer feel cold.
Storing: Wrap unsliced cake in plastic wrap and refrigerate for up to 2 days. Store sliced pieces in an airtight container in the refrigerator for up to 5 days.
Freeze: Wrap the cake roll in plastic and store it in a resealable plastic bag for up to 1 month. Defrost in the refrigerator until no longer solid, about 3 to 4 hours or overnight. Defrost at room temperature for 45 to 60 minutes. Sprinkle with powdered sugar right before slicing and serving.