Preheat the oven to 350 degrees Fahrenheit. Spray an 8-inch round cake pan with baking spray. Line the pan with parchment paper and spray the parchment paper as well.
In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, pumpkin pie spice, cinnamon, and salt. Set aside.
In a medium bowl, whisk together the olive oil, granulated sugar, brown sugar, eggs, pumpkin puree, and vanilla extract until just combined.
Pour the wet ingredients into the dry ingredients. Gently fold with a rubber spatula or mix on low speed until just combined.
Pour the batter into the prepared cake pan and spread evenly with an offset spatula. Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Place the cake pan on a wire rack and allow it to cool completely. Once cooled, run a knife around the edge of the pan to loosen the cake and carefully remove it. Make sure the cake is completely cool before frosting.
Sift together the powdered sugar and cinnamon. Set aside.
In the bowl of an electric mixer fitted with a paddle attachment, or using a hand mixer in a large bowl, beat the butter and cream cheese until smooth, creamy, and fluffy. Add the vanilla extract and salt, and mix to combine.
Turn the mixer off and gradually add the powdered sugar mixture. Beat on low speed until the powdered sugar is fully incorporated. Increase the speed to medium-high and beat for one minute until light and fluffy.
Use the frosting immediately or cover with plastic wrap or store in an airtight container in the refrigerator for up to 4 days.