Preheat oven to 350°F and spray three 8-inch cake pans with baking spray.
Cream butter on medium speed with a stand mixer or hand-held mixer until smooth. Add granulated and brown sugars; cream until fluffy and lighter in color. Add maple syrup and vanilla; mix well. Add eggs and mix until just combined.
In a medium-sized bowl, whisk together flour, baking powder, baking soda, salt, and apple pie spice. Add half of flour mixture to the butter mixture along with half of the milk and all of the oil. Mix until just combined. Add the second half of the flour mixture and milk. Mix until all ingredients are incorporated.
Divide batter evenly between the prepared cake pans and bake 15-18 minutes, or until a toothpick inserted into the center of the cake layers comes out clean. Let cakes cool in pans for 10-15 minutes, then invert onto a wire rack to cool completely.
For the frosting
Once the cake layers are cool, make the frosting. In a large bowl with a hand-held mixer or in the bowl of a stand mixer, beat cream cheese on medium speed until smooth. With mixer running, add butter a few slices at a time until fully incorporated. Add vanilla and mix well.
Add two cups of powdered sugar and one tablespoon of heavy cream. Mix on low speed until powdered sugar is mostly incorporated, and then medium-high speed until well combined. Scrapes the sides of the bowl and repeat with two more cups of powdered sugar and 1 tablespoon of heavy cream. Add the last two cups of powdered sugar and mix until incorporated and frosting is fluffy and smooth.
Spread a smear of frosting on the center of your cake plate to prevent cake from shifting while frosting. Place the first cake layer on top. Pipe or spread frosting over cake layer. Repeat with the remaining cake layers.
Transfer the cake to the fridge for 20-30 minutes to let the frosting firm up a little. This will help keep the cake layers from shifting while frosting the rest of the cake!
Once the frosting is a little more firm, spread frosting around the outside and over the top of the cake. Use an offset spatula or a spoon to create large swoops. If you have some frosting remaining, use an open piping tip to decorated around the edges.
Store cake in the refrigerator until ready to serve.