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1. In a medium bowl stir together flour, baking soda, and salt. In a large bowl beat granulated sugar and butter with an electric mixer on medium to high speed until fluffy, scraping sides of bowl occasionally. Beat in egg, lemon peel, lemon juice, rosemary, and lemon extract. Beat in as much of the flour mixture as you can with the mixer. Using a wooden spoon, stir in any remaining flour mixture.
2. Divide dough into four portions. Shape each dough portion into a 6-inch-long log. Wrap each log in waxed paper; twist the ends. Chill for at least 4 hours or up to 3 days. (Or freeze for up to 2 months.)
3. Preheat oven to 350 degrees F. Line cookie sheets with parchment paper; set aside. Cut chilled or frozen logs into 1/4-inch slices. Place slices about 1 inch apart on prepared cookie sheets. Bake for 8 to 10 minutes or until edges are lightly browned. Cool on cookie sheets for 2 minutes.
4. Place powdered sugar in a small bowl. Working in batches of two or three cookies, add warm cookies to the powdered sugar, turning to coat. Transfer to wire racks; cool. (To serve today, omit Step 5.)
5. Layer powdered sugar-coated cookies between sheets of waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months. Thaw cookies before serving.