How to Make It
Preheat oven to 375°F. Lightly spray a 10- x 15-inch jelly-roll pan with cooking spray. Line greased pan with parchment paper; lightly spray parchment paper.
Whisk eggs in a medium bowl until lightly beaten. Whisk in granulated sugar, oil, pumpkin, and pumpkin pie spice until well blended.
Whisk together flour and baking powder in another medium bowl. Whisk flour mixture into pumpkin mixture until smooth and well blended. Spread batter in an even layer in prepared jelly-roll pan. Bake in preheated oven until a wooden pick inserted in the center of cake comes out clean and edges of cake begin to pull away from pan, about 15 minutes. Remove from oven, and let stand in pan until cool enough to handle, about 10 minutes.
Lightly dust a clean linen towel with powdered sugar. Turn cake out onto prepared towel, and remove and discard parchment paper from cake. Trim crisp edges, if necessary. Starting with 1 short end, carefully roll up cake and towel, jelly-roll fashion. Set on wire rack, seam side down, and cool completely, about 1 hour.
Beat cream cheese and butter with an electric mixer on medium speed until combined and smooth. Add powdered sugar and vanilla, and beat until smooth, about 1 minute.
Unroll and remove towel from pumpkin roll; spread pumpkin roll with cream cheese mixture, and reroll. Garnish with a light dusting of powdered sugar just before serving.