In a small mixing bowl, sift together the flour, baking powder, salt, cinnamon, and nutmeg.
In a medium mixing bowl, add the eggs and sugar. Using a hand held mixer on medium-high speed, beat the eggs until they are light, pale yellow, and the consistency of soft whipped cream. This make take 5 to 10 minutes. Add the pumpkin puree and vanilla extract and beat on medium-low speed until just combined.
Sprinkle 1/3 of the dry ingredients over the eggs. Using a spatula, gently fold the dry ingredients until no dry streaks remain. Repeat this two more times.
Pour the batter evenly into the prepared baking sheet. Gently smooth out with the spatula - making sure to get the batter even and into the corners.
Bake the cake for 8 to 10 minutes - a toothpick inserted in the middle should come out clean. The cake will be spongy and springy when gently touched with your finger. Do not overbake the cake!
Cool the cake in the pan set on a wire cooling rack for about 2 minutes. Then, use the parchment paper to carefully lift the cake out of the pan. The cake should still be warm - almost hot - but not too hot to handle.
Rolling the cake - while the cake is warm and with the parchment paper still on it - start rolling the cake at the shorter end. Set the cake roll on the wire cooling rack to cool completely. The cake needs to be rolled while it is warm so it rolls, un-rolls, and re-rolls without cracking.