Preheat the oven to 350°F. Prepare three 6-inch cake pans or two 8-inch cake pans by spraying the sides with baking spray and fitting a wax or parchment paper circle to the bottom of the pans. Alternatively, you can grease and lightly flour the pans.
Using a food processor, grind the oatmeal into fine crumbs and place them into a medium bowl. Add the cake flour, baking powder, baking soda, cinnamon, and salt. Whisk to combine and set aside.
In the bowl of your stand mixer (a handheld mixer works fine too!), cream the butter on high until creamy, about 2 minutes. Add the vegetable oil, granulated sugar, and brown sugar and continue mixing on medium-high for another 2 minutes. Scrape down the bowl and paddle.
Turn the mixer to low speed and mix in the eggs one at a time. Add the sour cream and vanilla, then turn the mixer to high speed and beat for 1 minute.
With the mixer on low speed, add in the dry ingredients and mix until just combined, then add the milk in a slow stream and mix until just incorporated. Scrape down the sides and bottom of the bowl and give it a few stirs by hand to make sure there are no large lumps. The batter will be thick.
Divide the batter evenly between the prepared cake pans and bake for 30-35 minutes. They're done when they spring back to the touch and a toothpick inserted into the middle comes out clean. Let the cakes cool in the pan for five minutes before turning them out onto a wire rack for an additional few hours of cooling. Make sure they're entirely room temperature before applying any frosting.