Preheat the oven to 325 degrees . In a large bowl, whisk together the flour, 3/4 cup granulated sugar, the pumpkin pie spice, baking powder and salt. In a medium bowl, combine the egg yolks and pumpkin puree. Stir the pumpkin mixture into the flour mixture until smooth.
Using an electric mixer with the whisk attachment, whip the 9 egg whites at medium speed until foamy, about 2 minutes. With the machine on, gradually whisk in the remaining 1/2 cup granulated sugar; increase the speed to high and beat until stiff but still moist, 1 to 2 minutes.
Add one-quarter of the egg-white mixture to the pumpkin batter, folding with a rubber spatula just until no streaks remain. Repeat with the remaining egg white mixture. Pour the batter into a 10-inch tube pan with a removable bottom. Bake until a cake tester inserted in the center comes out clean, 55 minutes.
Let cool for 5 minutes, then invert the pan onto a narrow-necked bottle; let hang upside down until completely cool, about 1 1/2 hours. Place the cake right side up and remove the pan. To serve, dust with confectioners sugar.