Preheat oven to 350 degrees. Fill cupcake pan with liners.
Sift together flour, baking powder, and salt.
Whisk together buttermilk and egg whites in a medium bowl.
Put the sugar and lemon zest in a mixer bowl or another large bowl and rub them together with your fingers until the sugar is moist and fragrant.
Add the butter and, working with the paddle or whisk attachment (or hand mixer), beat and medium speed for 3 minutes, until the butter and sugar are very light.
Beat in the extract and lemon juice, then add one third of the flour mixture, still beating on medium speed. Beat in half of the buttermilk-egg mixture, then beat in half of the remaining dry ingredients until incorporated. Add the rest of the buttermilk and eggs, beating until the batter is homogeneous, then add the last of the dry ingredients.
Beat the batter for about 2 minutes to ensure that it is thoroughly mixed and well aerated. Fill the liners 1/2 full. Bake for 15-20 minutes, or until a toothpick comes out clean. Cool the cupcakes completely before frosting them.
Place the butter into a mixing bowl. Add 4 cups of the sugar and then the milk, vanilla, and lemon juice. On the medium speed of an electric mixer, beat until smooth and creamy, about 3-5 minutes.
Gradually add the remaining sugar, 1 cup at a time, beating well after each addition until the frosting is thick enough to be of good spreading consistency.
Add the peppermint extract and beat just until incorporated. If you would like, add yellow food coloring to the frosting and mix thoroughly.
*For me, I felt that the frosting wasn't as thick as I would like (since I pipe the frosting). It all depends on what consistency you would like. Add more powdered sugar until you get your desired consistency.*