Preheat oven to 325 degrees. Line 12 cupcake tins with paper liners.
Stir together the flour, baking powder and salt; set aside.
With an electric mixer, beat the butter until creamy, about 4 minutes.
Add the sugar, and beat for about another 4 minutes, scraping the sides of the bowl from time to time.
Beat in the vanilla.
Beat in the eggs, one at a time, scraping the sides of the bowl after each addition.
Add the flour mixture in 3 additions, beating on low speed just until smooth.
Spoon the batter into the cupcakes, and bake for about 22-27 minutes. Cakes should be golden on top and a toothpick inserted into the middle should come out clean.
Let cool in pan on a rack for 5 minutes, then remove and cool completely on a rack.