Preheat oven to 350 degrees F (177 degrees C) and place rack in center of oven.  Line two baking sheets with parchment paper.

For Cookies: Cream 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 and lemon zest. 

In a separate bowl whisk together the flour, baking powder, and salt.  Add to the butter and egg mixture and beat until combined.

Place the dough on a lightly floured surface and, with a floured rolling pan, roll out the dough to a thickness of 1/2 inch (1.25 cm).  Using cookie cutters, cut the dough into shapes.  Save the scraps and reroll.  Transfer  the cookies to the prepared baking sheet, spacing them a few inches apart.

Bake for approximately 8-10 minutes (baking time will vary depending on the size and shape of cookies) or until the bottoms of the cookies are lightly browned and a toothpick inserted into the center of a cookie comes out clean.  Remove from oven and place on a wire rack to cool.   Once the cookies have completely cooled, frost with icing.

For Frosting: In an electric mixer, cream the butter until smooth and well blended.  Add the vanilla extract.  With the mixer on low speed, gradually beat in the sugar.  Scrape down the sides of the bowl.  Add the milk and beat on high speed until frosting is light and fluffy (about 3-4 minutes).  Add a little more milk or sugar, if needed.  Tint the frosting with desired food color (I use the paste food coloring that is available at cake decorating stores and party stores).

Makes about 18 - 2 1/2 inch (6 cm) cookies.