Set the oven rack to the middle position. Heat the oven to 350ºF (177ºC).

Grease a 13 x 9-inch baking pan with cooking spray or vegetable oil. Add 1 tablespoon of flour to the pan, turn, and tap to lightly coat. Tap out any extra flour.

In a medium bowl, whisk together flour, pumpkin pie spice, baking powder, baking soda, and salt.

In a large bowl, whisk together granulated sugar, brown sugar, eggs, and vegetable oil until thick and smooth, about 3 minutes. Add pumpkin puree and whisk until combined.

Fold the flour mixture into the pumpkin mixture and stir until no flour streaks remain.

Spread the batter into the prepared baking pan. Bake until a toothpick comes out clean, about 30 to 33 minutes. Cool completely on a wire rack for 1 ½ to 2 hours.

In a stand mixer, beat softened butter and powdered sugar on low speed until just incorporated. Gradually increase speed to medium until light and fluffy, about 1 to 1 ½ minutes.

Add half of the cream cheese and beat until incorporated. Add remainder and beat until smooth.

Add maple syrup and vanilla extract. Beat until frosting is light and smooth.

Frost the cake directly in the pan or invert onto a serving platter. Spread cream cheese frosting evenly on top. Sprinkle with nuts if desired. Slice and serve.