Preheat oven to 350°F (180°C) and grease and flour a 9x13-inch baking pan.
In a medium bowl combine, flour, baking powder, baking soda, salt, and pumpkin spice.
In the bowl of a stand mixer fitted with the paddle attachment, whisk together oil, eggs, granulated sugar, and brown sugar at medium-high speed until thick and creamy, about 4 minutes.
Reduce speed to low and add pumpkin puree. Beat until combined.
With the mixer running on low add the flour mixture in three additions. Mix until just combined. Don't overmix.
Pour batter into prepared pan and bake in the middle of the oven for 35-40 minutes or until a toothpick inserted in the center comes out clean.
Transfer pan to a cooling rack and let cool completely.
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment beat butter and cream cheese until smooth.
Add vanilla and powdered sugar, mix on low until combined, then increase speed to medium-high and beat for 2 minutes.
Frost cake and serve. Cake can be refrigerated for up to 4 days. Let get to room temperature before serving.