Preheat oven to 350°F. Grease a 9x13-inch pan with cooking spray, and line with parchment paper. Spray top of parchment with more cooking spray.
Add flour, baking powder, salt, and sugar to the bowl of a stand mixer fitted with the paddle attachment. Mix on low speed for about 10 seconds, just to combine the ingredients
Combine the milk and sour cream in a large (2-cup) liquid measuring cup.
Add butter slices, oil, vanilla, and half of the milk mixture to the bowl of the stand mixer. Beat on medium speed until the mixture looks slightly crumbly. Stop the mixer and scrape down the sides of the bowl.
If you haven't separated your eggs already, crack the egg whites into the liquid measuring cup with the remaining milk/sour cream mixture (save the egg yolks for another recipe, like this French Silk Pie). Whisk to combine. With the mixer running on low speed, slowly add the milk mixture, in 2 additions, beating for 15 seconds in between each addition. Stop the mixer and scrape down the bowl once everything is incorporated.
Add in the sprinkles and mix for an additional 15 seconds on medium speed. Pour batter into prepared pan. Bake 35 to 40 minutes or until the sides pull away from the pan and a toothpick inserted into the center of the cake comes out clean.
Cool cake completely in pan. Once cooled, remove from pan and cool completely on a wire rack before frosting.