Adjust oven rack to middle position and preheat to 400 degrees F . Combine butter, coconut oil, sugar, salt, baking powder, and vanilla in the bowl of a stand mixer fitted with the paddle attachment. Mix at low speed to combine, then increase to medium and beat until soft, fluffy, and pale, about 5 minutes, although the exact timing will vary. Halfway through, pausing to scrape the bowl and beater with a flexible spatula, and then resume mixing on medium speed. Add the egg and continue beating until smooth. Reduce speed to low, add flour, and mix to form a stiff dough.
