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1
Position racks in the upper and lower thirds of the oven and preheat to 375 degrees F. Line 2 baking sheets with parchment paper and coat with cooking spray.
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2
Whisk the flour, baking powder, baking soda and 1/4 teaspoon salt in a medium bowl.
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3
Beat 6 tablespoons butter and the granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes.
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4
Add the egg and beat until combined.
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5
Reduce the mixer speed to low; beat in the flour mixture in two batches, alternating with the milk and vanilla, until just combined.
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6
Arrange mounds of batter (about 1 heaping tablespoonful each) about 2 inches apart on the prepared baking sheets; shape into rounds with damp fingers.
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7
Bake, switching the pans halfway through, until the tops of the cookies spring back when pressed, 9 to 12 minutes.
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8
Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely.
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9
Meanwhile, beat the remaining 6 tablespoons butter, the peppermint extract and the remaining pinch of salt in a large bowl with a mixer on medium speed until creamy, about 2 minutes.
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10
Gradually beat in the confectioners' sugar until smooth.
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11
Spread 1 1/2 tablespoons filling on the flat side of half of the cookies; sandwich with the remaining cookies.
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12
Roll the edges in the crushed candy canes.
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13
Photograph by Levi Brown
