Stained Glass Sugar Cookies

Whisk together flour and salt in a small bowl.

Beat together butter and sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 3 minutes in a standing mixer (preferably fitted with paddle attachment) or 6 minutes with a handheld, then beat in egg and vanilla. Add flour mixture and mix at low speed until just combined.

Form dough into 2 disks and chill, each disk wrapped in plastic wrap, until firm, at least 2 hours.

While dough chills, unwrap candies and separate by color in small heavy-duty sealable plastic bags. Seal bags, forcing out air, then coarsely crush candies by wrapping each bag in a kitchen towel and pounding bags with a rolling pin.

Preheat oven to 350F.

Roll out 1 piece of dough into a 9-inch round (1/8 inch thick) on a well-floured surface with floured rolling pin (keep remaining dough chilled). Cut out as many cookies as possible from dough with a large cutter (about a 2-inch cutter) and transfer to a parchment-paper-lined baking sheet, arranging cookies about 1 inch apart. Cut out centers from cookies with small cutter (about 3/4 to 1-inch) and add to scraps. Spoon about 1/2 to 1 teaspoon crushed candy (depending on size of cutout) in center of each cookie. (If you want to use these cookies as tree ornaments, make a hole with a drinking straw at the top of the cookie for hanging.)

Bake in middle of oven until edges are golden, 10 to 12 minutes, then cool cookies completely on baking sheet on a rack, about 10 minutes. Transfer with a metal spatula to a plate or an airtight container. Gather scraps and chill until firm enough to re-roll, 10 to 15 minutes. Make more cookies with remaining dough and scraps (re-roll once) in same manner on cooled baking sheet. Cookies keep, layered between sheets of wax paper or parchment paper, in an airtight container at room temperature, 1 week.

Make ahead: Dough can be chilled up to 3 days.