Preheat oven to 375°F (190°C). Grease a 15x10-inch jelly roll pan, line with parchment paper, and grease the parchment. Lay a thin cotton towel flat and sift 1/4 cup powdered sugar evenly over it.
In a small bowl, whisk together flour, baking powder, baking soda, cinnamon, ginger, cloves, and salt. Set aside.
In a large bowl, beat eggs on high speed for 3 to 4 minutes until pale and thick. Gradually beat in granulated sugar until the mixture holds a ribbon when the beaters are lifted.
Beat in pumpkin puree and lemon juice until fully combined. Add the dry ingredients and stir with a spatula just until no streaks of flour remain, without overmixing.
Pour batter into the prepared pan and spread into an even layer with an offset spatula, all the way to the corners. Bake for 13 to 15 minutes, until the top springs back lightly when touched and edges just start to pull from the pan.
Immediately run a knife around the edges to loosen, then flip the cake out onto the sugared towel. Peel off parchment, then starting from a short end, roll the cake up together with the towel into a tight spiral.
Place the rolled cake seam side down on a wire rack and let it cool completely at room temperature, about 1 hour. Do not unroll during this time.
Beat softened cream cheese and butter together until smooth. Add powdered sugar and vanilla, and beat again until light and fluffy with no lumps.
Carefully unroll the cooled cake and set the towel aside. Spread filling evenly over the cake, leaving a half-inch border, then sprinkle with chopped nuts if using. Re-roll the cake without the towel, starting from the same short end, and place seam side down on a serving plate.
Wrap the rolled cake in plastic wrap and refrigerate for at least 1 hour, until the filling firms up. Dust with powdered sugar just before slicing into rounds with a serrated knife.