Chocolate Peppermint Stars

Make Buttery Sugar Cookie dough as directed, but reduce the flour to 1 1/3 cups and add the cocoa.

Whisk the flour and cocoa together.

Halve dough and wrap each half in wax paper, shaping each into a flattened rectangle, then store each half in a resealable plastic bag. Chill dough until firm, at least 2 hours.

Heat oven to 350°F with rack in middle. Line baking sheets with parchment paper.

While oven heats, roll out 1 piece of dough (keep remaining dough chilled) between two large sheets of wax paper to slightly less than 1/4 inch thick. (If dough becomes too soft to roll out, quick-chill on a baking sheet in the freezer or chill in the refrigerator until firm.)

Peel back top sheet of wax paper and cut out as many cookies with cutter as possible.

Transfer cookies, as cut, to a lined baking sheet, arranging them 1 inch apart. (If dough becomes too soft to remove the cookies, quick-chill on a baking sheet in the freezer or chill in the refrigerator until firm.)

Gather, reroll, and chill scraps to form more cookies.

Freeze or chill cut-out cookies on baking sheet until firm before baking.

Bake cookies, one sheet at time, until edges are a shade darker and centers are set, 9 to 12 minutes. For picture-perfect cookies, use cookie cutters while cookies are hot from the oven to trim edges. (Keep trimmings for snacks.)

Transfer cookies with a metal spatula to racks to cool completely. Make more cookies with remaining dough. (Cool baking sheets and use fresh parchment between batches.)

Using the offset spatula or a small rubber spatula, spread cooled cookies with a thin layer of melted chocolate, then sprinkle with some crushed candy canes.

Let cookies stand at room temperature until the chocolate has set, about 1 hour.

•If you want a real hit of peppermint, replace the vanilla in the Buttery Sugar Cookie dough recipe with 1/2 teaspoon pure peppermint extract.•For the cleanest edges, keep freezing or chilling the dough between the sheets of wax paper whenever it gets soft, and freeze or chill the cut-out cookies before baking them.•To melt chocolate successfully: Keep chocolate from coming in contact with even the smallest amount of water. Chop the chocolate first, then put it in a dry metal bowl and set the bowl over a pan of barely simmering water.

Heat the chocolate, stirring occasionally, until it is smooth. Alternatively, you can heat it in a microwave-safe bowl.

Put the chopped chocolate in the bowl and microwave it at 50% power at 30-second intervals, checking it and stirring it, each time, until it is smooth.•Cookies keep in an airtight container in single layers, separated by wax paper, in a cool place, 5 days.