Glazed Lemon Cookies

Sugar Cookies

1. Cream together the butter and sugar in a large bowl with an electric mixer on high speed for 1 minute. Add the egg and mix well. Mix in the vanilla, lemon extract, and salt.
2. In a separate bowl, whisk together the flour, baking powder, and baking soda. Pour dry mixture into the wet mixture and mix well with the mixer until no more flour is visible.
3. Turn out dough onto counter and knead gently by hand until smooth, about 10 seconds. Divide dough in half. Place 1 piece of dough in center of large sheet of parchment paper and press into 7- by 9-inch oval. Place second large sheet of parchment over dough and roll dough into 10- by 14-inch oval of even thickness. Transfer dough with parchment to rimmed baking sheet. Repeat pressing and rolling with second piece of dough, then stack on top of first piece on sheet. Refrigerate until dough is firm, at least 1 ½ hours (or freeze for 30 minutes). (Rolled dough can be wrapped in plastic wrap and refrigerated for up to 5 days.)
4. Adjust oven rack to lower-middle position and heat oven to 300 degrees. Line rimless cookie sheet with parchment. Working with 1 piece of rolled dough, gently peel off top layer of parchment. Replace parchment, loosely covering dough. (Peeling off parchment and returning it will make cutting and removing cookies easier.) Turn over dough and parchment and gently peel off and discard second piece of parchment. Using cookie cutter, cut dough into shapes. Transfer shapes to prepared cookie sheet, spacing them about ½ inch apart. Bake until cookies are lightly and evenly browned around edges, 14 to 17 minutes, rotating sheet halfway through baking. Let cookies cool on sheet for 5 minutes. Using wide metal spatula, transfer cookies to wire rack and let cool completely. Repeat cutting and baking with remaining dough. (Dough scraps can be patted together, rerolled, and chilled once before cutting and baking.)

Lemon Icing

1. Make the icing by combining the powdered sugar, lemon juice, milk, and lemon extract in a medium bowl.
2. Use a small frosting knife or back of a spoon to coat the top of each cooled cookie with icing. 
3. Let the icing set up for about an hour before frosting cookies.