Preheat the oven to 375°F. Coat the wells of a doughnut pan with non-stick cooking spray.
In a bowl, whisk together the flour, baking powder, baking soda and salt. In a measuring cup, stir together the buttermilk and whole milk. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium speed until light and fluffy, about 2 minutes. Scrape down the sides of the bowl. Add the egg and vanilla; beat on medium speed until combined, about 1 minute. On low speed, add the flour mixture in 3 additions, alternating with the milk mixture and beginning and ending with the flour. Beat each addition until just blended. Fold in the sprinkles.
Pour 2 tablespoons batter into each prepared well. Bake, rotating the pan 180 degrees halfway through baking, until a toothpick inserted into the doughnuts comes out clean, about 10 minutes. Let cool in the pan on a cooling rack for 5 minutes, then invert the doughnuts onto the rack and let cool completely.
Meanwhile, wash and dry the pan and repeat to bake the remaining batter.
Line a baking sheet with parchment paper. Dip the doughnuts, top side down, into the glaze. Place, glazed side up, on the prepared baking sheet, decorate with sprinkles, and serve.
Courtesy of The Doughnut Cookbook by Williams-Sonoma Test Kitchen