Sift the flour into a medium bowl (if using cup measures, spoon into the cups and level with a knife before sifting).
Combine the butter, coconut oil, sugar, salt, baking powder, nutmeg, and vanilla in the bowl of a stand mixer fitted with a paddle attachment.
Mix on low speed to moisten, then increase to medium and beat until light and fluffy, about 5 minutes, pausing to scrape with a flexible spatula halfway through.
With the mixer running, crack in the egg and continue beating until smooth.
Reduce the speed to low, add the flour, and mix to form a stiff dough.
Divide into thirteen 2½-ounce (¼-cup) portions or twenty-six 1¼-ounce (2-tablespoon) portions.