Preheat oven to 350F (175C) and prepare 3 8-inch round cake pans by generously greasing and flouring. Be sure to shake out excess flour.

In stand mixer, beat butter on medium-low speed until creamy.

Add sugar and oil and beat until all ingredients are well-combined and creamy.

Scrape down the sides and bottom of the bowl and then stir in your vanilla.

In separate bowl, whisk together your flour, baking powder, and salt.

Measure out your milk.

With mixer on medium speed, gradually alternate between adding the flour mixture and the milk to the butter mixture, starting and ending with the flour mixture. Stir until each one is almost completely combined before adding the next.

Pause occasionally to scrape down sides and bottom of bowl.

In separate bowl, combine your egg whites and, with a hand-mixer on high-speed, beat until stiff peaks form.

Using a spatula, gently fold your egg whites and sprinkles into your batter. Take care to scrape the sides and bottom of the bowl so that ingredients are well-combined, and take care not to over-mix.

Evenly divide cake batter into prepared pans.

Bake on 350F (175C) for 35-40 minutes, or until a toothpick inserted in the center of each cake layer comes out clean or with few crumbs (should not be wet). For best results, rotate your cake pans halfway through baking to ensure even baking.

Cakes will be a light golden brown when done baking.

Remove cakes from oven and allow to cool for 15 minutes. Run a butterknife around the inside rim of each pan and invert each onto a cooling rack.

Allow to cool completely before frosting.

Frosting

I used this technique from I Am Baker to frost my cake. If you intend to use this technique as well it requires a lot of icing for the top and I recommend increasing this recipe by 50%. If you are just doing a plain covering that will not be needed.

In stand mixer, beat butter on medium-speed until creamy.

Add salt and beat again for about 20 seconds.

Gradually, about 1 cup at a time, add powdered sugar, waiting until each cup is completely mixed before adding the next cup.

Tbsp at a time, add the heavy cream on medium-high speed, waiting until each addition is well-combined before adding the next 2 Tbsp.

Add flavoring (vanilla extract or emulsion). and stir on medium-high for 30 seconds.

Transfer one layer of your cooled cake to serving platter. Use frosting to ice the top. Add the next layer, ice the top of that. Add your third layer on top and ice the top, and then do a thin "crumb coating" around the entire cake.

Transfer to freezer for 10-15 minutes, then remove and apply a clean, thick coat of frosting around the entire cake.