1Cream together 1 cup butter and white sugar. Beat in the egg and 1 teaspoon vanilla. Combine together the sifted flour, salt and ground cinnamon and stir into butter mixture.
2Cover and chill dough for 3 hours.
3Preheat oven to 350 degrees F (175 degrees C).
4Lightly flour a rolling pin. Roll out dough on lightly floured wax paper and cut with cookie cutter. As dough warms it becomes unworkable. Return to refrigerator as needed. Bake on ungreased cookie sheet 15-20 minutes until lightly browned.
5To Make Icing: Sift confectioners' sugar into mixing bowl. Add vanilla, salt, and butter. Add milk one tablespoon at a time while beating until spreadable consistency. Continue beating on medium for 10 minutes. Ice cookies.