Preheat oven to 350˚F (180˚C). Lightly grease 2-3 doughnut pans.
In a large bowl, whisk together the flour, sugar, cornstarch, baking powder, baking soda, salt, and nutmeg.
Make a well in the center and add the buttermilk, egg, butter, and vanilla bean paste.
Mix into the flour mixture just until incorporated with no lumps.
Gently fold in the rainbow sprinkles.
Transfer the batter to a piping bag or a large ziploc bag with the corner snipped off.
Pipe the batter into prepared doughnut pans. Each cavity should be about 2/3 full.
Bake the donuts in the preheated oven until golden and the tops spring back when lightly pressed, 12-14 minutes.
Allow to cool in the pan for 5 minutes, then transfer to wire rack to cool completely to room temperature.
To make the vanilla glaze:
In a medium bowl, whisk together the powdered sugar, milk, and vanilla bean paste until smooth. If too thin, add more powdered sugar. If too thick, add more milk.
Immediately dip the tops of a few cooled doughnuts into the glaze and add a few sprinkles. Allow to set briefly before serving.
To make the chocolate glaze:
In a medium bowl, whisk together the powdered sugar and cocoa powder. Stir in milk and vanilla bean paste until smooth. If too thick, add a little more milk. If too loose, add a little more powdered sugar.
Immediately dip the tops of the doughnuts in the glaze and add a few sprinkles. Allow to set briefly before serving.