Heat the oven to 350 F and set a rack in the center. Leave the 15x10x1 inch jelly roll pan ungreased.

In a large bowl, whisk the flour, baking powder, baking soda, cinnamon, pumpkin pie spice and salt until evenly combined. Set aside.

In a second large bowl, whisk the eggs, granulated sugar and brown sugar until the mixture lightens slightly, about 1 minute. Whisk in the oil, pumpkin puree and vanilla until completely smooth with no streaks of pumpkin.

Add the dry mixture to the wet and stir with a rubber spatula just until the last of the flour disappears. Do not use a mixer here and do not beat. Overmixing whips in air that expands and collapses, sinking the center.

Pour the batter into the ungreased pan. It will look thin. Spread it into the corners with an offset spatula and level the top.

Bake 25 to 30 minutes, until the surface springs back when pressed lightly and a toothpick inserted in the center comes out clean with no wet batter.

Set the pan on a wire rack and cool completely, at least 1 hour. Frosting a warm slab will melt it straight off the edges.

Beat the softened cream cheese, butter and vanilla with an electric mixer on medium until fluffy and no lumps remain, about 2 minutes.

Add the powdered sugar 1 cup at a time on low speed, then beat on medium until smooth and spreadable, about 1 minute more.

Spread the frosting evenly over the cooled slab with an offset spatula, working all the way to the edges.

Refrigerate uncovered about 1 hour, until the frosting sets firm. Cut into 24 squares with a clean knife, wiping the blade between cuts. Serve chilled or at room temperature.