Preheat oven to 350 degrees F (177 degrees C) and line 12 muffin cups with paper liners.
In the bowl of your electric mixer, or with a hand mixer, beat the butter and sugar until light and fluffy. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla extract.
In a separate bowl whisk together the lemon zest, flour, baking soda, and salt.
With the mixer on low speed, alternately add the flour mixture and milk, in three additions, beginning and ending with the flour. Scrape down the sides of the bowl as needed.
Evenly fill the muffin cups with the batter and bake for about 1 hour and 30 minutes or just until set and a toothpick inserted into a cake comes out clean. (Always check a few minutes before the stated baking time. Do not over bake or the cupcakes will be dry.) Remove from oven and place on a wire rack to cool. Once the cupcakes have completely cooled, frost with icing. If you want flat topped cupcakes then slice off the dome of each cupcake, with a sharp knife, before frosting. If you want to pipe the frosting, I like to use a large Wilton 1M star decorating tip. Cupcakes are best eaten the same day they are made, but they can be covered and stored for a few days.