1. Combine the flour and salt in a medium bowl. Beat the butter and sugar in a large mixing bowl at medium speed until light and fluffy. Add the egg, lemon peel, and vanilla and beat until blended. At low speed beat in flour mixture until just combined. Divide dough into quarters. Wrap each piece in plastic wrap and refrigerate until well chilled, 1 hour or overnight.
2. Heat oven to 350 degree F. Grease 4 cookie sheets. Between 2 sheets of lightly floured waxed paper, roll one dough quarter 1/8-inch thick, keeping remaining dough refrigerated. Remove waxed paper and cut with floured cookie cutters into desired shapes. Transfer cut-outs to prepared cookie sheets. Bake until edges are golden, 8 to 9 minutes. Transfer the cookies to wire racks to cool completely. Repeat, rolling and cutting remaining dough, rerolling scraps. Decorate as desired. Makes about 1-1/2 dozen 4-inch cookies.