In a medium mixing bowl whisk together the flour, baking powder, and salt. Set aside.
In a stand mixer fitted with a paddle attachment, cream together the butter and sugar. Add the eggs one at a time, beating between each addition. Add vanilla and mix until combined.
Add the dry ingredients in three parts, alternating with milk. The dough should be soft but not sticky.
Cover the dough and chill in the refrigerator for one hour.
Preheat oven to 350°F and line a baking sheet with parchment paper and set aside.
Remove the dough from the refrigerator and roll out on a lightly floured surface so it's ¼-inch thick. Using a lightly floured donut cutter, cut out shapes (donuts and holes) from the dough and place them on the prepared baking sheet.
Bake for 10 to 12 minutes until lightly brown around the bottoms. Allow them to cool on the cookie sheet for a few minutes before transferring to a wire rack to cool completely.
While the cookies are cooling, whisk together the icing ingredients until smooth, add the milk 1 tbsp at a time until desired consistency is reached. Add red food coloring if you like.
Once cookies have cooled, dip them in the glaze and then directly into the sprinkles. Place on a cooling rack to set.