Prepare oven and jellyroll pan: Preheat oven to 350°F. Lightly coat a 15- x 10-inch jellyroll pan with cooking spray, and line bottom of pan with parchment paper. Lightly coat parchment with cooking spray.

Make cake batter: Whisk together eggs, granulated sugar, pumpkin, and 1 ½ teaspoons of the vanilla in a large bowl until well combined. Whisk together flour, pumpkin pie spice, baking powder, and ½ teaspoon of the salt in a small bowl until well combined. Gradually sift flour mixture over egg mixture, folding just until combined and no flour pockets remain.

Add batter to jellyroll pan: Pour batter into prepared pan, spreading in an even layer with a small offset spatula.

Bake cake: Bake in preheated oven until center of cake springs back when pressed with a finger lightly coated with cooking spray, about 12 minutes.

Prepare towel for rolling: While cake bakes, lay a clean linen towel that measures at least 16- x 12-inches on a work surface; sift ¼ cup of the powdered sugar in a 16- x 12-inch rectangle on towel.

Roll cake: Turn cake immediately onto sugar-coated towel; carefully remove and discard parchment. Starting with one short end, gently and slowly roll up cake and towel together, jellyroll style. Let cool completely on a wire rack in towel, seam side down, about 2 hours. Cake can be stored, loosely covered with plastic wrap, at room temperature up to 18 hours.

Make filling: Fill a medium saucepan with water to a depth of 1 inch. Bring saucepan to a boil over medium-high, then reduce heat to a simmer over medium-low. Place white chocolate in a medium glass heatproof bowl, and place bowl on top of saucepan, making sure bottom of bowl doesn’t touch water. Cook over medium-low, stirring often and adjusting heat as needed to maintain a simmer, until chocolate is melted, about 5 minutes. Remove bowl from heat, and slowly add cream cheese in 1-ounce increments, stirring after each addition until completely melted, smooth, and combined. (The mixture will look a bit broken, but it will come back together later when the powdered sugar is added.) Stir in 1 cup of the powdered sugar, remaining ½ teaspoon vanilla, and remaining ¼ teaspoon salt. Chill, covered, until frosting is firm enough to spread, about 1 hour.

Add frosting to cake, and roll again: Very carefully unroll cake; spread frosting evenly on top, leaving a ½-inch border on all sides. Reroll cake without towel, and transfer, seam side down, to a platter. Trim edges, if desired. Dust with remaining ¼ cup powdered sugar. Leftovers can be stored, covered, in refrigerator up to 3 days.