Heat the oven to 350 degrees.
Generously coat a mini doughnut pan with butter and dust with flour (GF: be sure entire pan is coated in butter, including top and sides any overflow might touch. GF flour sticks more so you want to be sure it pops right out).
Sift the cake flour, baking powder, and salt into a large mixing bowl (GF: also add in xantham gum).
Beat in the butter one 1/2 teaspoonful at a time, using a stand mixer set on low speed, until the mixture resembles coarse meal.
Beat in the sugar a tablespoon at a time, until the mixture looks like fine sand.
Beat in eggs one at a time.
Add vanilla and the milk, and beat on medium-high, just until blended.
Do not overbeat or your doughnuts will be tough and chewy.
Pour into doughnut cavities- only about 1/4-1/2 full so they don't over rise. (GF: this is extremely important! It is easier to remove if it doesn't spill over onto the sides of the pan when rising).
Bake until slightly browned- about 15 minutes. (GF: let it brown just a touch over normal for easier removal. Add on a minute or two at most.)
Cool cakes in the pan on a wire rack until cool to the touch and doughnuts pop out when teased with a fork or knife.
Frost with pourable icing- recipes found at: http://sweetcsdesigns.com/homemade-pourable-icing/