Preheat your oven to 350 degrees F. Grease a 9-inch cake pan or springform pan with Pam's Baking Spray. Line the bottom with parchment paper and spray the sides. Set aside.
In a medium-sized bowl, whisk together the flour, baking powder, pumpkin pie spice, cardamom, ground cinnamon, ground ginger, nutmeg, and salt. Set this dry mixture aside.
In a stand mixer fitted with the paddle attachment, cream together the granulated sugar, brown sugar, and eggs on medium speed until light and fluffy, which should take about 4 minutes.
Add the vegetable oil and vanilla extract, and beat on medium speed until fully incorporated (approximately 30 seconds). Then, add the pumpkin puree and mix until well combined (about 30 seconds).
With the mixer on low speed, gradually add the dry ingredients to the pumpkin and egg mixture. Mix until just combined.
Pour the pumpkin batter into the prepared springform pan. Set aside while you make the cream cheese filling.
For the Cream Cheese Filling
In a medium-sized bowl, use a hand mixer on medium-high speed to beat the cream cheese until it's smooth and creamy.
Add the egg and mix on high for 30 seconds, using a rubber spatula to scrape the sides and bottom of the bowl.
Add the pumpkin pie spice and cinnamon, then gradually add 1 cup of powdered sugar at a time, mixing for 30 seconds after each addition. This should take a little over 1 minute to complete.
Once combined, pour the cream cheese mixture on top of the pumpkin cake batter and use a small offset spatula to spread it into an even layer.
Bake for 40-45 minutes. The middle of the cake will still be slightly jiggly, but it's done when the edges are golden and the middle has cracked.
When the cake is done, let it cool for 10-15 minutes, then place it in the fridge to chill for at least 2 hours to allow the cream cheese to firm up and set.