Preheat the oven to 350°F with a rack in the center position. Line only the bottom of an 8x2-inch round cake pan with parchment paper, and set it aside. Do not spray or grease the pan.
Spread all the pumpkin purée evenly on a baking sheet* and bake for 45 minutes. Immediately transfer the roasted purée* to a large mixing bowl and chill it for a few minutes until lukewarm or cooler.
To a separate, small bowl, add the all-purpose flour, baking powder, table salt, and pumpkin spice. Whisk for about 30 seconds. Set aside.
In a large mixing bowl, whisk the egg yolks, caster sugar*** (labeled: for yolks), roasted pumpkin purée, and cooking oil until combined. Set aside.
Add the egg whites to a medium mixing bowl, and have the caster sugar (labeled: for whites) nearby. Use a hand-mixer or stand mixer to whip on medium-high speed (7 of 10 on my hand mixer). Do not mix at the highest speed. At 15 seconds, the egg whites should start to foam. Keep whipping while slowly incorporating the sugar into the foamy egg whites until stiff peaks.^ This can take 6 to 10 minutes, depending on your mixer.
Sift the dry ingredient mixture into the pumpkin mixture and whisk until most of the flour is no longer visible. I like to use the same beaters I used on the meringue to whisk here.
Scoop a silicone spatula-full of meringue into the pumpkin mixture and mix until completely combined. This prepares the batter for folding.^^ Then, gently fold a third of the meringue into the pumpkin batter until there are no more white streaks. Repeat with half of the remaining meringue, and then the remainder.
Pour the batter into the cake pan lined at the bottom with parchment paper. Do not line the sides, and do not spray the pan. Use the silicone spatula or an offset spatula to smooth the top. Bake on the center rack for 55 minutes.
Remove the cake from the oven and place it on a wire rack to cool. Once the pan is cool enough to hold in your hands, use an offset spatula or other narrow tool to release the sides of the cake. Turn the cake out of the pan and allow to cool completely.
Once the cake is completely cool, place a large mixing bowl in the freezer^^^ and prepare the ingredients for the Chantilly frosting.