Use a coffee or spice grinder to pulverize the spice pods.
5.75 ounces all-purpose flour (about 1 1/4 cups)
1 teaspoon baking powder
1 teaspoon freshly ground star anise (about 3 pods)
1/4 teaspoon salt
1/4 teaspoon cream of tartar
6 tablespoons unsalted butter, softened
1 cup plus 2 tablespoons sugar, divided
1/2 teaspoon vanilla extract
1 large egg
3/4 teaspoon ground cinnamon
How to Make It
Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 4 ingredients (through cream of tartar); stir with a whisk. Place butter in a medium bowl; beat with a mixer at medium speed 30 seconds or until smooth. Add 1 cup sugar and vanilla; beat until well combined. Add egg; beat 1 minute or until well combined. Add flour mixture; beat at low speed 30 seconds. Shape dough into a ball; wrap in plastic wrap. Chill 1 hour.
Arrange 1 oven rack 2 positions down from top of oven; arrange another rack 2 positions up from bottom of oven. Preheat oven to 375°.
Shape dough into 24 balls. Combine remaining 2 tablespoons sugar and cinnamon in a shallow dish. Roll dough balls in cinnamon mixture, coating completely. Place balls 3 inches apart on 2 parchment-lined baking sheets. Bake at 375° for 11 minutes or until edges are golden, rotating pans after 6 minutes. Cool on pans for 5 minutes. Remove cookies from pans; cool on wire racks.