Heat the oven to 350°F. Coat a rimmed half baking sheet (18x13-inches) with cooking spray. Line the bottom with a sheet of parchment paper.
Whisk 1 ⅓ cups all-purpose flour, 2 teaspoons ground cinnamon, 1 teaspoon baking powder, ¾ teaspoon ground ginger, ½ teaspoon baking soda, ¼ teaspoon ground cloves, ⅛ teaspoon ground nutmeg, and ⅛ teaspoon black pepper together in a medium bowl.
Whisk 1 cup granulated sugar, 1 cup pumpkin purée, ½ cup packed light brown sugar, 3 room-temperature large eggs, 3 tablespoons neutral oil, 1 ½ teaspoons vanilla extract, and ¾ teaspoon kosher salt together in a large bowl until smooth.
Sift the flour mixture through a fine-mesh strainer into the pumpkin mixture. Fold with a flexible spatula until just combined and no dry bits remain.
Transfer the batter onto the baking sheet. Use the flexible spatula or an offset spatula to smooth the batter into an even layer. Tap the pan against the counter a few times to release any large air bubbles and even the batter.
Bake until puffed and a tester inserted into the center comes out clean, 12 to 15 minutes. Meanwhile, have a clean kitchen towel (at least the size of the baking sheet) ready.
Immediately after taking the cake out of the oven, run an offset spatula or paring knife around the cake to loosen the edges. Place ¼ cup powdered sugar in a fine-mesh strainer and dust it generously over the cake. Lay the kitchen towel over the cake, making sure it is completely covered. Place a second baking sheet or large cutting board (at least the size of the baking sheet) on top.
Grasping the baking sheet and what’s on top at the same time to hold them together (careful, hot!), flip it over in one motion. Remove the baking sheet and the parchment. Slide the cake, still on the towel, onto the work surface. Starting with one of the shorter sides, carefully roll the cake up in the towel to create a tight, neat spiral (like rolling up dough for cinnamon rolls). Be careful not to squish the cake when rolling.
Place the towel-wrapped cake on a wire rack seam-side down. Let cool completely, about 1 ½ hours. Meanwhile, make the filling.
Beat 4 ounces room-temperature cream cheese, ¾ cup powdered sugar, 1 ½ teaspoons vanilla extract or paste, and ¼ teaspoon kosher salt with the whisk attachment in a stand mixer on medium speed until combined and smooth, scraping down the bowl as needed, about 30 seconds.
Reduce the speed to medium-low. Slowly pour in 1 cup cold heavy cream. Increase the speed to medium-high and beat, scraping down the bowl as needed, until stiff peaks form, about 45 seconds. Refrigerate until the cake is cooled.
Carefully unroll the cake. It will want to roll back up — do not press it flat. Give the chilled filling a few good stirs, then spread evenly over the cake.
Carefully re-roll the cake, without the towel, going in the same direction it was rolled for cooling. I use a serrated knife to trim the ends to reveal a nice, neat spiral (eat the trimmings as a snack).
Transfer the cake to a serving platter seam-side down. Lightly dust with powdered sugar. For clean slices, use a serrated knife and sawing motions to cut, and wipe the knife between slices.
