Adjust oven rack to middle position and heat oven to 350 degrees F. Lightly spray 18- by 13-inch rimmed baking sheet (a half sheet pan) with non-stick cooking spray, line with parchment paper and spray the parchment lightly with another layer of non-stick cooking spray.
Whisk flour, pumpkin pie spice, baking soda, and salt in medium bowl; set aside. With electric stand mixer fitted with the paddle attachment on medium-high speed, beat eggs and sugar until pale yellow and thick, 6 to 10 minutes. Add pumpkin and mix on low until incorporated. Fold in flour mixture until just combined and no flour streaks remain. Pour batter into prepared pan and evenly spread. Bake until cake is firm and springs back when touched, about 15 minutes. As soon as the cake comes out of the oven, run a paring knife around edge of cake to loosen. Move pan to a wire rack until cooled completely, about 1 hour.
For the Whipped Cream & Cream Cheese Frosting:
Add the cream cheese, powdered sugar, and vanilla to the bowl of a stand mixer fitted with the paddle attachment. Mix on low until combined, then increase speed to medium-high and beat until smooth & creamy, about 1 minute. Transfer mixture to a small bowl; set aside.
In the bowl of a stand mixer fitted with the whisk attachment, add the chilled cream and beat until stiff speaks form. Add the cream cheese mixture and mix on low until just combined.
Use a paring knife to cut the cake into 4 even pieces running the width of the cake (see image above). Use a small spatula to loosen each cake piece from the parchment.
Spread each piece with a generous portion of the frosting, about 1/2 cup on each piece.
Starting with the first piece of cake, gently tuck the cake into a roll. Line the end seam up with the beginning of the next piece of cake and roll. Repeat with the remaining cake strips.
Place the cake on a cake plate or pedestal and cover with the remaining frosting, leaving the top uncovered. Chill the cake for at least 3 hours before serving.
Pumpkin Cake adapted from Cook's Country & the Whipped Cream & Cream Cheese Frosting is a Food Folks and Fun original!