Butter Cookies: In the bowl of your electric mixer, or with a hand mixer, beat the butter and sugar until light and fluffy.  Beat in the egg, zest, and vanilla extract. 

In a separate bowl, whisk together the flour and salt. Gradually add the flour mixture to the creamed mixture and beat just until incorporated. Scrape down the sides of the bowl as needed. Divide the dough in half and shape each half into a log (round or square) that is about 1 1/2 inches (4 cm) in diameter. Wrap each log in plastic wrap and place in the refrigerator until firm (at least two hours or preferably overnight). (Can freeze the unbaked logs for up to two months.) Once the log is firm, with a sharp knife, slice cookies about 1/8 - 1/4 inch (.3-.5 mm) thick.

Preheat oven to 350 degrees F (177 degrees C). Place oven rack in the center of the oven. Line a baking sheet with parchment paper. 

Place the cookies on the baking sheet, spacing about 2 inches (5 cm) apart. If you like, make an egg wash by beating one egg white with 1 teaspoon water. Brush cookies with the egg wash and sprinkle with chopped nuts or colored sugar. Bake the cookies for about 10-15 minutes, or until the edges of the cookies are golden brown. Remove from oven and place on a wire rack to cool. Unfrosted, these cookies can be stored several weeks at room temperature.

Frosting: In the bowl of your electric mixer, or with a hand mixer, beat the butter and shortening until smooth and well blended. Beat in 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 until frosting is of spreading consistency. Add more milk or sugar, if needed. Can tint portions of frosting with desired food color.

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