Preheat the oven to 350°F (177°C) and grease a 9×13-inch baking pan.
Whisk the flour, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice together in a large bowl. Set aside. Whisk the oil, eggs, brown sugar, granulated sugar, pumpkin, and vanilla extract together until combined. Pour the wet ingredients into the dry ingredients and use a mixer or whisk until completely combined. Batter will be thick.
Spread batter into the prepared pan. Bake for 30-36 minutes. The cake is done when a toothpick inserted in the center comes out clean. If the top or edges are browning too quickly, loosely cover with aluminum foil.
Remove the cake from the oven and set the entire pan on a wire rack. Allow to cool completely. After about 45 minutes, place the cake in the refrigerator to speed things up.
Make the frosting: In a large bowl using a handheld or stand mixer, beat the cream cheese and butter together on high speed until smooth and creamy. Add 3 cups confectioners' sugar, vanilla, and salt. Beat on low speed for 30 seconds, then switch to high speed and beat for 2 minutes. If desired, add the extra ¼ cup of confectioners sugar for a thicker frosting.
Spread the frosting on the cooled cake. Refrigerate for 30 minutes before serving.
Cover leftover cake tightly and store in the refrigerator for 5 days.
