Preheat oven to 350˚F (180˚C). Line a 12-cup muffin pan with paper liners. In a medium bowl, whisk flour, baking powder, and salt together. In the bowl of a stand mixer fitted with the paddle attachment or in a large bowl using an electric hand mixer, beat butter on medium-high speed until smooth, about 1 minute. Add granulated sugar and beat until creamy, about 4 minutes more. Scrape down sides of bowl, then beat in eggs, one at a time, then the vanilla.
With the mixer on low speed, beat in the flour mixture in three batches, alternating with milk in two batches. Increase speed to medium-high and beat until just combined, scraping the sides of the bowl if necessary.
Spoon batter into muffin cups, filling each three-quarters full. Bake until tops of cupcakes spring back when pressed gently, 20 to 25 minutes.
Remove pan from oven. Let cupcakes cool for 5 minutes in the pan, then remove from pan and let cool completely on a rack.