Add butter and sugar to the bowl of a stand mixer and mix on low or 1 minute. Increase speed to medium for 1 minute, then back to low speed.
Add the eggs one at a time, beating until each one is incorporated. Mix in the vanilla extract.
In a medium mixing bowl whisk together the flour, cake flour, baking soda, cornstarch, and salt. Slowly add the dry ingredients to the bowl of wet ingredients. Alternate adding the flour mixture with milk so it blends easier. Mix until combined on low speed.
Cover the dough and place in the refrigerator for one hour.
To Bake the Cookies
Preheat the oven to 350°F and line a baking sheet with parchment paper or a baking silicone mat.
Remove the dough from the refrigerator and roll out on a lightly floured surface to 1/4" thickness. Cut out your cookies (3-4" is a good size).
Use a small circle cookie cutter, cut out shapes (donuts and holes) from the dough.
Place the baking sheet with cookies in the fridge to chill for 10 minutes before baking.
Bake for 10 to 12 minutes until lightly brown around the bottoms. Allow them to cool on the cookie sheet until room temperature.
To Make the Icing
In a medium bowl, whisk together the dry ingredients for the frosting. Add liquid ingredients and whisk until you have a smooth chocolate glaze.
Once cookies have cooled, dip the top of each cookie in the glaze and then into the sprinkles.
Allow to dry for 30 minutes.
Notes
Nutritional information is provided as an estimate only and will vary based on exact ingredients used and serving size.