Scrape seeds from vanilla bean into a small food processor. Add sugar, anise seeds, and lemon peel; cover and pulse several times to combine.

In a large mixing bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar mixture and lemon juice. Beat until fluffy, scraping bowl occasionally. Beat in flour and salt until combined. Divide dough in half. Cover and chill 1 hour or until dough is easy to handle.

Preheat oven to 275 degrees F. On a lightly floured surface, roll half the dough at a time to 1/2 inch thick. Using a 2- to 2-1/2-inch fluted round cookie cutter, cut out dough. Sprinkle cookies with cinnamon sugar. Place cutouts on an ungreased cookie sheet. Bake in the preheated oven for 35 to 40 minutes or until edges are firm to the touch. Cool on cookie sheet 2 minutes. Transfer cookies to a wire rack; let cool. Spoon Lemon Glaze evenly over cookies. Let cookies stand until glaze is set. Makes 18 cookies.

In a medium bowl, combine 2 cups powdered sugar, 2 tablespoons milk and 1 tablespoon lemon juice. Beat together with an electric mixer on medium speed until combined. Add more milk, if necessary, to make a spoonable glaze.

Use lime juice in place of the lemon juice in this cookie.

Layer 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.