Whisk the cake flour, baking powder, and salt in a medium bowl and set aside.
Add the softened butter to a large bowl or bowl of a stand mixer. Use an electric mixer or the paddle attachment to beat the butter until smooth and creamy. Gradually add the granulated sugar and mix on low speed until all of it is added in. Then, mix on medium speed until the sugar and butter are combined, light, and fluffy. Add the vegetable oil and mix until combined.
Add the room temperature eggs, one at a time, and mix on low speed until just combined after each. Add the vanilla extract and whole milk and mix until smooth. Wipe the sides of the bowl with a rubber spatula as needed.
In 3-4 additions, add the dry ingredients to the batter and mix on low speed until just incorporated after each, then mix until smooth once all of the dry ingredients are added. Don't overmix.
Divide the batter evenly between the three prepared cake pans. Gently tap the pans on the counter to spread the batter out evenly and get rid of any trapped air bubbles. For the best results, try wrapping the pans with cake strips*, which help the cakes bake evenly so they don't have a domed top.
Bake the cakes in the preheated oven for 18-22 minutes, or until a toothpick inserted into the center comes out clean. Allow the cakes to cool in the pan before removing, then cool completely in the fridge or freezer before assembling.