Heat oven to 375°F and line a 15×10-inch jelly-roll pan with parchment; lightly grease the paper. Whisk flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Beat eggs and granulated sugar 3–5 minutes until light and thick. Mix in pumpkin and 1 teaspoon vanilla, then fold in the dry mixture just until combined.
Spread batter evenly and bake at 375°F for 13–15 minutes until the center springs back and a tester shows no wet batter.
Within about 2–3 minutes, lift the warm cake and roll from a short edge with parchment inside. Cool seam-side down on a rack for about 60 minutes.
Fill and Chill
Beat cream cheese, powdered sugar, and the remaining 1 teaspoon vanilla until smooth; stir in nuts if using. Gently unroll cooled cake and spread filling evenly, leaving a small border.
Reroll while removing parchment, wrap, and refrigerate at least 60 minutes until firm. Cut into 10 slices.
Notes
Refrigerate the filled roll and use within 3–4 days.
Keep cream cheese-filled slices at room temperature for no more than 2 hours.
Freeze tightly wrapped for up to 2 months and thaw in the refrigerator.