Beat butter and sugar on medium speed for 2 minutes until fluffy. Scrape the bowl once.

Mix in the egg and vanilla on low, then add the whisked dry ingredients in two additions, folding the last streaks by hand.

Roll half the dough on a floured surface to ¼-inch thickness, cut shapes, and transfer to a parchment-lined sheet. Repeat with remaining dough, pressing scraps together once.

Bake at 350°F (180°C) for 8 to 10 minutes, until bottoms are pale gold. Cool on the sheet for 2 minutes, then move to a wire rack.

Stir together powdered sugar, 2 tsp milk, and vanilla for the glaze, adding more milk if needed. Spread onto completely cooled cookies and add sprinkles.