When the browned butter/coconut oil mixture has solidified and become opaque again (but is still nice and creamy, i.e. whippable) transfer it to the bowl of a stand mixer fitted with the paddle attachment. Add the sugar, salt, baking powder, cardamom, and vanilla to the butter mixture and mix on low speed to moisten. Increase to medium speed and beat until light and fluffy; about 5 minutes, stopping to scrape the sides of the bowl halfway through. With the mixer running, add the egg and continue beating just until smooth. Reduce the speed to low, add the flour, and mix just until a stiff dough forms.