Beat butter and granulated sugar in large bowl with electric mixer on medium speed until light and fluffy. Add egg, 1/2 teaspoon of the extract and salt; mix well. Gradually beat in flour on low speed until well mixed. Divide dough in half. Form each half into a log about 9 inches long and 1 1/2 inches in diameter. Wrap in plastic wrap. Refrigerate 1 hour.
Preheat oven to 350°F. Cut dough into 1/4-inch slices. Place 1 inch apart on ungreased baking sheets.
Bake 12 minutes or until edges are lightly browned. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.
For the Glaze, mix confectioners' sugar, water and remaining 1/4 teaspoon extract until smooth. Drizzle over cooled cookies. Let stand until glaze is set.