• Preheat the oven to 350°F. Grease and line a 9”x13” cake pan with parchment paper.
• In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt. Add the milk, eggs, and vanilla extract and whisk until combined. 
• Add the melted butter and oil. Whisk the batter until the fats begin to emulsify into the batter, then switch to a large rubber spatula or wooden spoon. Continue to stir until smooth. It is okay if a few lumps remain.
• Tip the mixture into the prepared pan. Bake for 27 to 32 minutes or until a toothpick inserted comes out clean or with a few moist crumbs. Completely cool the cake before frosting.

For the Vanilla Buttercream

• Using a stand (or hand) mixer fitted with the paddle attachment, beat butter on medium-low speed until smooth and creamy (1 to 3 minutes). 
• Stop the mixer and add 3 cups of confectioners' sugar. Mix in the sugar on low speed until just combined. Add 2 tablespoons of milk and vanilla extract and mix until blended.
• Turn the mixer up to medium-high speed and mix for 3 to 5 minutes, until the buttercream is light, airy, and nearly white. If needed, add the additional confectioners’ sugar or milk until desired consistency is achieved. The buttercream should spread smoothly without tearing the crumb of the cake.
• Reduce the mixer speed to low and mix for about a minute or two to smooth out the air bubbles.