In a small bowl, combine sugar and cinnamon. Pour 1/2 cup of this mixture into a small, shallow bowl. In a spice grinder, grind anise seeds until they are finely ground.
Beat butter, shortening, salt, remaining 1/2 cup of cinnamon sugar mixture and ground anise seeds in the the bowl of a stand mixer fitted with the paddle attachment on medium-high speed until fluffy, about 3 minutes. Scrape down bowl as needed. Add the egg yolk and vanilla and continue to beat until combined. Reduce the speed to low and add the flour. Mix until a dough begins to form, about 10-12 seconds.
Roll dough into a 9-inch circle, 1/2-inch thick on a sheet of parchment paper. Transfer the dough on the parchment to a large baking sheet and refrigerate until firm, about 25-30 minutes.
Place oven racks in upper-middle and lower-middle positions. Preheat oven to 350 degrees. Line two large baking sheets with parchment. Transfer chilled dough to cutting board. Cut into shapes using cookie cutter or pizza cutter. Space evenly on prepared sheets, about 20 per sheet.
Bake for about 15 minutes, or until cookies are set and just beginning to brown, switching trays halfway through. Let cookies cool for just 5 minutes on tray. Gently toss warm cookies in reserved cinnamon sugar mixture. Transfer to wire rack to cool completely.