Combine first 3 ingredients in a large bowl; stir with a whisk until sugar dissolves. Add egg; stir with a whisk until smooth. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt in a medium bowl, stirring with a whisk. Add flour mixture to sugar mixture; stir until smooth. Cover and chill 1 hour.
Preheat oven to 300°.
Coat baking sheets with cooking spray or line with parchment paper. Shape 1 1/2 teaspoons of dough into a 2-inch log. Connect ends of log together, forming a ring; place on prepared baking sheets. Repeat procedure with remaining dough, placing 1 inch apart. Bake at 300° for 15 minutes or until edges are golden brown. Remove cookies from pans; cool on wire racks. Sprinkle cookies evenly with powdered sugar while still warm.
3 More Ways with Anisette Liqueur:
Stir into coffee.
Heat, mix with powdered sugar, and drizzle over warm pound cake.
Add a splash to steaming liquid for shellfish like mussels or clams.