Preheat the oven to 350˚F and line a muffin tin with paper muffin liners. In a large measuring cup, whisk together eggs, egg yolk, vanilla, and buttermilk. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, whisk together the flour, sugar, baking powder, and salt.
Mix the dry ingredients on low speed. Cut the butter into small pieces and drop into the running mixer.
Run until the butter is fully incorporated into the dry ingredients and the mixture resembles coarse crumbs.
At low speed, slowly pour the buttermilk mixture into the flour. When all of the liquid has been added, increase the speed to medium and beat until the batter is light and fluffy, about 2 minutes.
Divide the batter into the prepared pan. Bake the cupcakes for 18 to 25 minutes, until golden brown and a cake tester inserted into the center of a cupcake comes out clean. Let cool in the pan for 10 minutes, then cool completely on a wire rack, about 1 hour.