Prep the pan: Heat oven to 350°F (175°C). Lightly grease a 6-cavity doughnut pan with nonstick spray or a thin film of oil.
Whisk dry ingredients: In a medium bowl, whisk 1 1/2 cups all-purpose flour, 1/2 cup granulated sugar, 1 1/2 teaspoons baking powder, and 1/4 teaspoon fine salt.
Mix wet ingredients: In another bowl, whisk 3/4 cup buttermilk, 1 large egg, 3 tablespoons melted unsalted butter (slightly cooled), and 2 teaspoons vanilla extract until smooth.
Combine: Pour wet ingredients into dry. Stir gently with a spatula just until no dry streaks remain. Do not overmix; a few small lumps are fine.
Fill the pan: Transfer batter to a piping bag or a zip-top bag with the corner snipped. Pipe into the prepared cavities, filling each about 2/3 full. This helps keep the holes open and the shape even.
Bake: Bake for 9–11 minutes, until the tops spring back when lightly pressed and a toothpick comes out clean or with a few moist crumbs.
Cool: Let doughnuts rest in the pan for 2 minutes, then turn out onto a wire rack to cool completely before glazing.
Make the glaze: In a shallow bowl, whisk 1 1/2 cups powdered sugar, 2–3 tablespoons milk or cream, 1 teaspoon vanilla extract, and a tiny pinch of salt. Adjust with more sugar to thicken or a drip of milk to thin. You want a pourable, shiny glaze that clings.
Dip and decorate: Dip the top of each cooled doughnut into the glaze. Let excess drip off, then place back on the rack. Immediately add sprinkles so they stick before the glaze sets.
Set and serve: Allow glaze to set for 15–20 minutes. Enjoy fresh or store as directed bel