In a large bowl, with a mixer on medium speed, beat shortening and 3/4 cup sugar until smooth. Add egg, orange peel, and orange juice and beat just until combined.
In a medium bowl, mix 2 1/2 cups flour, anise seeds, baking powder, and salt. Add to shortening mixture, stir to mix, then beat until well blended. Divide dough in half and flatten each half into a disk. Wrap each disk tightly in plastic wrap and freeze until firm, about 30 minutes.
Unwrap dough. On a lightly floured surface, with a floured rolling pin, roll one disk at a time to about 1/8 inch thick. With floured cookie cutters, cut dough into shapes and place about 1 inch apart on buttered 12- by 15-inch baking sheets. Gather excess dough into a ball, reroll, and cut out remaining cookies.
In a small bowl, mix remaining 1/4 cup sugar and the cinnamon. Sprinkle about 1/8 teaspoon of the mixture over each cookie; save any remaining cinnamon sugar for other uses.
Bake cookies in a 350° regular or convection oven just until edges are golden, 10 to 12 minutes; if baking two sheets at once in one oven, switch their positions halfway through baking. Let cookies cool on sheets for 5 minutes, then use a wide spatula to transfer to racks to cool completely.
Nutritional analysis per cookie.