Preheat oven to 350°F (175°C). Line a muffin pan with cupcake liners.
In the bowl of a stand mixer, sift together cake flour, baking powder, baking soda, and salt. Whisk in the sugar.
With the mixer on low, add the cubed butter a few pieces at a time, then drizzle in the oil. Mix until mixture resembles damp sand.
In a separate jug, whisk egg whites, whole egg, buttermilk, and vanilla.
With mixer on low, add half the wet ingredients to the dry. Mix to combine, then beat on medium for 90 seconds.
Scrape bowl. With mixer on low, add remaining wet ingredients, mixing until just combined and smooth.
Fill liners 2/3 full. Bake for 17-20 minutes, until a toothpick comes out clean. Cool in pan 5 mins, then transfer to wire rack to cool completely.