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Preheat oven to 175F.
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Line two baking sheets with parchment paper.
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Fit a pastry bag with a small open-star tip (such as Ateco #22).
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Make meringues: Put egg whites and sugar in the heatproof bowl of an electric mixer.
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Set bowl over a pan of simmering water, and stir gently until sugar has dissolved and mixture is warm to the touch, 2 to 3 minutes.
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Transfer bowl to an electric mixer fitted with the whisk attachment.
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Mix on medium-high speed until stiff peaks form.
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Mix in peppermint extract.
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Using a new small paintbrush, paint two or three stripes of red gel-paste food coloring inside the pastry bag.
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Fill bag with 1 to 2 cups meringue.
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Pipe small (3/4-inch high) star shapes onto prepared baking sheets.
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Refill bag as necessary, adding food coloring each time.
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Bake cookies until crisp but not brown, about 1 hour 40 minutes.
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Let cool completely on sheets on wire racks.
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Meanwhile, make ganache: Heat cream in a small saucepan over medium-low heat until just simmering.
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Pour over chocolate in a small bowl.
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Let stand 5 minutes.
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Gently stir until smooth, about 5 minutes.
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Let ganache cool at room temperature, stirring every 5 to 10 minutes, until thick enough to hold its shape, about 45 minutes.
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(If ganache sets before using, reheat in a heatproof bowl set over a pan of simmering water; repeat the cooling process.)
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Fill a pastry bag fitted with a small plain round tip (such as Ateco #5) with ganache.
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Pipe a small amount onto bottom of one meringue.
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Sandwich with another.
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Repeat with remaining ganache and meringues.
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Transfer to wire racks; let set 30 minutes.
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Cookies can be stored in a single layer in airtight containers at room temperature up to 2 days.
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Use a new small paintbrush to brush two or three evenly spaced stripes of gel-paste food coloring along the length of the inside of a pastry bag fitted with an open-star tip.
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Fill the bag with meringue, and pipe star shapes onto a parchment paperlined baking sheet.
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Each time you refill the bag with meringue, paint new stripes inside.