Prep: Preheat oven to 350°F. Line two 6" round cake pans with a round of parchment paper on the bottom of each pan. Set aside.
Dry mixture: In a small bowl, stir together flour, baking powder, and salt. Set aside.
Hot milk mixture: In a small pot or microwave-safe bowl, add the butter, milk, oil, and vanilla extract. Heat it on the stovetop or in the microwave until the butter has melted. Don't let it boil. Remove it from the heat and cover to keep it warm while you start making the batter.
Beat eggs and sugar: In a large mixing bowl, add the eggs and sugar. Use an electric hand mixer fitted with a whisk attachment to beat the mixture for a full 6 minutes at medium speed or until the mixture has tripled in size and becomes very pale (almost white) in colour.
Combine dry and wet mixtures: Add half of the flour mixture and mix on low speed until just barely combined. Add the rest of the flour and mix until mostly combined. Some flour patches are fine because you'll continue mixing some more in the next step and we don't want to overmix.
Add hot milk mixture: With the mixer on low speed, slowly stream in the hot milk mixture until you have a smooth and fluid batter.
Fill pans: Divide the batter into your lined cake pans until about halfway full.
Bake: Bake cakes for about 35-40 minutes or until a toothpick inserted in the middle comes out mostly clean with a few crumbs.
Let cool: Let the cakes cool in the pans for about 15 minutes before running an offset spatula around the edges of the pan. Release the cakes onto a wire rack to cool completely.