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To make the cookies:
- In a food processor, combine the butter and flour and mix until crumbs form. Turn the dough out onto a floured surface and make a well.
- To the well add the sugar, baking powder, vanilla, egg, lemon zest and the rum.
- Mix with your hands until a dough forms.
- Form the dough into a disk and wrap in plastic wrap. Refrigerate for 1 hour.
- Preheat your oven to 350 degrees. Line a baking sheet with parchment paper.
- Roll the dough out between 2 pieces of parchment paper to about 1/4 inch thickness. Using a star cookie cutter, cut out as many cookies as possible. Re roll any scraps and cut out more cookies.
- If the dough becomes too sticky, refrigerate for 10 minutes and roll the dough out again.
- Place the cut out cookies on the parchment lined baking sheet. Bake for 8-10 minutes.
- Cool completely before glazing.
To make the glaze:
- In a bowl whisk together the confectioners sugar, milk and extract until a thick glaze forms. Drizzle the glaze over the cookies.
- For a more precise application, Fill a small plastic zipper top bag with the glaze. Snip a small corner off one side and pipe the glaze around the outline of the cookie and fill with more glaze. Decorate with colored nonpareils.