Preheat the oven to 350F (175C) and line the muffin pan with paper liners.
In a bowl, combine the flour, baking powder, and salt. Set aside.
Pour the oil into a microwave-safe bowl, add the butter, and heat just until the butter has melted. Then combine it with the milk and add vanilla extract. Set aside.
Place the eggs and white and brown sugar in a stand mixer fitted with a whisk attachment (or use a large bowl and a hand mixer). Whip on medium-high until the sugar has dissolved and the mixture tripled in volume. It will take approximately 7 minutes depending on what mixer you use.
Then, add the dry ingredients in 3 parts while the mixer is running on low just until incorporated and no flour is visible.
When done, take two tablespoons of the batter and add it to the milk mixture. Whisk until homogenous in consistency. Slowly pour everything back into the main batter while the mixer is running on low. Scrape the bottom and the sides of the bowl and mix on low for 10 seconds to combine.
Fill the cupcake liner ⅔ full and bake for 17-20 minutes or until a toothpick inserted in the middle of a cupcake comes out clean. Remove from the oven and leave to cool down in the pan for a few minutes. Then, transfer onto a cooling rack to cool down completely before frosting.