For the cookies:
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1 cup (2 sticks) unsalted butter, softened
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2/3 cup confectioners' sugar
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1 large egg yolk
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1/2 tsp vanilla extract
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1/2 tsp peppermint extract
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2 cups all-purpose flour
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1/4 cup cornstarch
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1 tsp baking powder
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1/2 tsp salt
For the frosting:
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3/4 cup (1 1/2 sticks) unsalted butter, softened
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1/4 tsp salt
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1 1/2 cups confectioners' sugar
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1 tsp vanilla extract
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1/2 tsp peppermint extract
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2 tbsp whole milk
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3/4 cup finely crushed peppermint candies or candy canes, to garnish
Steps
1
Make the cookies: In a large bowl, using a hand mixer or stand mixer, beat the butter on medium-high until smooth and creamy, 2–3 min. Gradually beat in the confectioners’ sugar on low until smooth, scraping down sides of bowl occasionally. Add the egg yolk and both extracts, and beat on medium-high until smooth. Add the flour, cornstarch, baking powder, and salt. Mix on low until just combined. Chill dough for at least 45 min., or up to 2 days.
2
Preheat oven to 350°F. Line 2 cookie sheets with parchment. Scoop out 2-tbsp balls of cookie dough and place on baking sheets, about 1 inch apart. Press each cookie-dough ball with the bottom of a glass to flatten slightly. Bake 13–15 min., until the edges are set. (Cookies will not brown.) Transfer to wire racks and cool completely.
3
Make the frosting: In a large bowl, beat the butter and salt until smooth and creamy. On medium-high speed, gradually beat in the confectioners’ sugar until smooth, scraping down sides of bowl occasionally. Gradually beat in the extracts and milk, 1 tbsp at a time, until desired consistency. Using a spatula or piping bag fitted with a tip, frost cookies and then top with crushed peppermint candies. Store in an airtight container at room temperature for up to 4 days.
Tips
To crush candy canes, use a food processor or place in a 1-gallon resealable bag and crush with a heavy skillet or rolling pin.