Preheat the oven to 350°F (177°C). Spray a 9x13 baking pan with nonstick cooking spray and set aside.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, pumpkin pie spice, ground cinnamon, and salt. Set aside.
In a separate bowl, whisk together the pumpkin puree, oil, brown sugar, granulated sugar, eggs, and vanilla until fully combined. Add the dry ingredients to the wet ingredients and mix until just combined.
Pour the batter into the prepared pan and spread it around into one even layer. Bake for 30 to 40 minutes or until a toothpick inserted into the center of the cake comes out clean. If needed, cover loosely with foil for the last 5 to 10 minutes of baking to prevent excess browning.
Remove from the oven and place the pan on a wire rack to cool completely.