Combine flour, baking powder, soda, and nutmeg in a large mixing bowl; cut in shortening with a pastry blender until mixture resembles coarse crumbs.
Combine eggs, sugar, milk, and vanilla in a small mixing bowl; mix well, and pour into crumb mixture. Stir with a fork until moistened. Shape into a ball. Chill 1 hour.
Divide dough in half, keeping one half chilled until ready to use. Roll to 1/8-inch thickness on a lightly floured surface; cut with assorted cookie cutters.
Place on lightly greased cookie sheets; bake at 375° for 5 minutes or until edges are lightly browned. Remove from cookie sheets, and cool on wire racks. Repeat procedure with remaining dough. Decorate as desired with Powdered Sugar Glaze.