Prepare the pan: Preheat the oven to 350°F (175°C). Line a 15 × 10-inch (38 × 25 cm) jelly roll pan with parchment paper, leaving an overhang for lifting out the baked cake.
Combine the dry ingredients: In a bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Beat the eggs and sugar: In a separate large bowl, beat the eggs and granulated sugar with an electric mixer until pale, thick, and fluffy. Add the pumpkin purée and vanilla extract, mixing until combined.
Finish the batter: Gently fold the dry ingredients into the pumpkin mixture just until no streaks of flour remain. Spread the batter evenly in the prepared pan, reaching into the corners.
Bake: Bake for 13-15 minutes, until the surface springs back when lightly touched and a toothpick inserted into the center comes out clean. Avoid overbaking.
Roll the warm sponge: Carefully lift the cake out using the parchment overhang. Starting at a short end, roll the hot sponge with the parchment still attached, keeping the paper between the layers. Place seam-side down on a wire rack and let cool completely, about 1 hour.
Make the filling: Beat the softened cream cheese and butter until smooth. Add the powdered sugar and vanilla extract. Mix on low speed until incorporated, then beat until smooth and creamy, scraping down the bowl as needed.
Fill and reroll: Gently unroll the cooled sponge without forcing the curled center flat. Spread the filling evenly over the cake, leaving a small border around the edges. Roll it up again, peeling away the parchment as you go so no paper remains inside.
Chill: Wrap the filled roll snugly in plastic wrap or parchment paper. Refrigerate seam-side down for at least 2 hours or overnight.
Slice and serve: Unwrap and dust lightly with powdered sugar, if desired. Slice with a sharp knife, wiping the blade between cuts, and serve chilled.
