Step 1Heat the oven to 350 degrees. Line standard muffin cups with paper liners.
Step 2In a medium bowl, sift together the flour with the baking powder and salt. In a small bowl or measuring cup, stir together the milk and vanilla extract. Set aside.
Step 3In the bowl of a stand mixer, or in a large bowl using a hand mixer, cream the butter. Gradually add in the sugar, beating until light and fluffy, about 5 minutes.
Step 4Beat in the eggs, one at a time, until fully incorporated. Beat in the flour and milk mixtures, alternating one-third of each at a time, until each mixture is fully incorporated and the batter is smooth.
Step 5Fill each muffin cup three-fourths full of batter. Bake the cupcakes until puffed, set and lightly golden, and a toothpick inserted comes out clean.
Step 6Cool the cupcakes before frosting.
Step 1In the bowl of a stand mixer, or in a large bowl using a hand mixer, beat the butter with one-half of the powdered sugar until combined. Beat in the milk and vanilla, scraping down the sides of the bowl, and beating until smooth.
Step 2With the mixer set to low speed, gently beat in the remaining sugar until combined. Increase the speed and continue to beat until the frosting is light and fluffy. This makes about 2 1/2 cups frosting.
Step 3Frost each cupcake with a generous 2 tablespoons frosting.