Preheat oven to 350 degrees; line the cups of a standard (12-cup) muffin tin with paper or foil liners. In a small bowl, whisk together flour, baking powder, and salt; set aside. In a liquid-measuring cup, mix milk and vanilla; set aside.
In a large bowl, with an electric mixer, beat butter and sugar until light and fluffy, 3 to 4 minutes. Add eggs one at a time, beating well after each addition. With mixer on low speed, add half of dry ingredients, followed by milk-vanilla mixture, then remaining dry ingredients. Do not overmix.
Divide batter evenly among prepared muffin cups (a 2-ounce or 1/4-cup ice-cream scoop is good for this).
Place tin on a rimmed baking sheet; bake until a toothpick inserted in center of a cupcake comes out clean, 20 to 25 minutes. Cool cupcakes 5 minutes in tin, then remove and cool completely on a rack before frosting.
Prepare frosting: In a medium bowl, with an electric mixer, beat butter, confectioners' sugar, milk, and vanilla extract until smooth. Mix in up to 1/2 cup more sugar or a few more teaspoons of milk as necessary to achieve a spreadable consistency. Makes enough for 12 cupcakes.
Frost cupcakes; decorate with sprinkles before frosting dries to ensure that they stick. The frosted cupcakes are best eaten within 1 day.