Prepare the baking pan. Preheat the oven to 375°F. Grease a 10 x 15-inch or 9½ x 14-inch jelly roll pan, then cover the bottom with parchment paper to prevent sticking and simplify removal.
Place the all-purpose flour, baking powder, cinnamon, pumpkin pie spice, nutmeg, and salt in a small bowl. Whisk thoroughly until evenly distributed, then set the mixture aside.
In a large mixing bowl, beat the eggs with the granulated sugar until the mixture becomes pale, thick, and fluffy. Add the pumpkin purée and continue beating until fully incorporated.
Add the prepared dry mixture to the pumpkin mixture. Blend only until no visible streaks of flour remain. Transfer the batter to the lined jelly roll pan and spread it into an even layer.
Place the pan in the preheated oven and bake for 14 to 16 minutes. The cake is ready when its surface springs back gently after being lightly pressed.
Leave the baked cake in the pan for 2 minutes. Carefully loosen the edges with a thin knife or spatula.
Lightly coat a second sheet of parchment paper with nonstick cooking spray. Invert the cake onto the prepared parchment and remove the parchment that lined the baking pan. Using the parchment for support, roll the cake from one short end to the other.
Position the wrapped cake seam-side down and allow it to cool fully in its rolled form. Cooling it this way establishes the spiral shape and reduces the likelihood of unrolling.
Beat the softened cream cheese and butter in a medium bowl until completely smooth and evenly combined. Add the confectioners’ sugar and vanilla extract, then continue beating until the filling is light and fluffy.
Carefully unroll the cooled pumpkin cake. Spread the cream cheese mixture evenly across the entire surface, reaching close to the edges.
Gently roll the cake again from the short end, enclosing the filling inside. Transfer it to a serving plate and position it seam-side down.
Trim both ends for a tidy presentation. Immediately before slicing, lightly dust the top with confectioners’ sugar. Add a small sprinkling of cinnamon when desired.