Preheat oven to 350F and prepare (2) 8" cake pans by lightly greasing and flouring the sides and lining the bottom with parchment paper. Set aside.
Combine butter and sugars in the bowl of a stand mixer (or in a large bowl and use an electric mixer). Beat until well-combined and light and fluffy.
Add oil and beat to combine.
Stir in pumpkin.
Add eggs, stirring well after each addition, and then add vanilla extract.
Add milk and stir to combine. Scrape down the sides and bottom of the bowl to ensure ingredients are evenly combined.
In a separate, medium-sized bowl, whisk together dry ingredients (flour, baking powder, baking soda, salt, pumpkin spice, and cinnamon).
Gradually add dry ingredients to wet, stirring until completely combined (be sure to scrape down the sides and bottom of the bowl). I prefer to do this with a spatula to avoid over-mixing the batter.
Divide batter evenly into prepared cake pans and bake on 350F for 35-45 minutes, or until centers spring back to the touch and a toothpick inserted in the center comes out with few moist crumbs or clean.
Allow cakes to cool for 10 minutes and then invert onto cooling rack and allow to cool completely before frosting.
Cream Cheese Frosting**
In KitchenAid (or with hand mixer) cream together butter and cream cheese.
Gradually add powdered sugar to mixture until well-combined.
Stir in vanilla bean seeds (or vanilla extract) and salt. Scrape down the sides and bottom of the bowl to ensure ingredients are well-combined.
Add heavy cream and gradually increase speed to medium-high. Beat for 30 seconds, until frosting is silky smooth.
Once cakes have cooled, ice/assemble cakes by generously icing between layers, applying an even layer on the top of the cake, and then applying a scant, semi-naked layer around the outside of the cake.
*This is slightly more than 1 15oz can of pumpkin puree. Make sure that you buy "100% pumpkin" and not "pumpkin pie filling"
**This cake was frosted in a "semi-naked" style, which means not a lot of frosting was used. If you want to completely frost the whole cake, I recommend increasing by 50% and you may wish to omit the heavy cream for a firmer frosting.