Preheat oven to 350°. In a small bowl, cream butter and sugar until light and fluffy, 3-5 minutes. Beat in lemon zest and vanilla. Combine the flour, cornstarch, nutmeg, and salt; gradually add to creamed mixture and mix well. (Dough will be crumbly.) Shape into a ball., On a lightly floured surface, press dough to 1/2-in. thickness. Cut with a floured 1-in. fluted cookie cutter; place 1 in. apart on ungreased baking sheets. Prick cookies with a fork. Reroll scraps if desired. , Bake until firm, 12-15 minutes. Cool for 2 minutes before carefully removing to wire racks to cool completely. , Combine confectioners' sugar and lemon juice; drizzle over cookies. Store in an airtight container.