Thoroughly stir together flour, anise, baking powder, and salt and set aside.
Using a small sharp knife, peel a thin layer of zest (without
white membrane) from the entire lemon.
Combine lemon zest and sugar in a food processor fitted with a steel blade. Process until zest is very finely minced.
Add shortening and butter to the processor and process for one minute. Add egg yolk and vanilla and process 20 seconds
longer.
Add dry ingredients and continue processing just until they are
blended.
Divide dough in half and place each portion between large sheets of waxed paper and roll out to 1/8 inch thick.
Check the underside of the dough to check for any creases. Slide dough onto a large tray or baking sheet and refrigerate for 15 minutes, or until the dough is chilled and slightly firm.
Preheat oven to 375 degrees F. Lightly grease several baking sheets.
Work one half of the dough at a time. Turn the dough over and peel the sheet of wax paper off of the dough and replace the paper loosely. Then turn the dough right side up. Peel off and discard the top sheet of paper.
Using assorted 2 1/4 to 3" cookie cutters cut out cookies.
Place in the oven and bake for 8-10 minutes or until just brown at the edges.
Remove from the oven and let stand for 3 minutes. Transfer to
wire racks and let stand until cooled completely.