Preheat oven to 350°F / 175°C.
Line a cupcake pan with cupcake liners. Set aside.
If you're making your own buttermilk, see the NOTE below and make it now. Set aside.
Whisk together the flour, baking powder, and salt. Set aside.
Using a hand mixer or a stand mixer, beat the butter and sugar until it's creamy.
Add the egg and vanilla to the butter mixture and mix well. Then add the buttermilk and oil and mix until everything is fully incorporated.
Add the dry ingredients to the wet ingredients and mix until JUST combined. Don't overmix.
Fill the cupcake liners with the batter, a little over halfway full. I like using a cookie scoop.
Bake for 18-20 minutes, or until a toothpick inserted in the center comes out clean.
When done, take the cupcakes out of the oven and allow them to cool in the pan for about 5 minutes before removing them to a wire rack to cool completley.
Make sure they are completely cool before frosting them.