This recipe is from Yvonne Ruperti of America's Test Kitchen
2 cups all-purpose flour, plus extra for work surface
3 teaspoons baking powder
1/2 teaspoon salt
8 tablespoons unsalted butter, softened
2 cups confectioners' sugar, divided
1 large egg
1 teaspoon peppermint extract
1 teaspoon red food coloring (gel or paste)
1 large egg white
Red sanding sugar
White sanding sugar
In a medium-size bowl, combine flour, baking powder, and salt; set aside. In the bowl of standing mixer, cream butter and 1 cup sugar until light and fluffy, about 3 minutes. Mix in egg. Reduce speed to low, and add egg and peppermint extract. Mix in flour mixture until just combined.
Divide dough into two pieces. Knead red food coloring into one piece, adding more food coloring if necessary. Keep one piece plain. Form each piece into a 4x4-inch square, wrap in plastic, and chill until firm, about 1 hour.
On a lightly floured work surface, roll out plain dough into a 6x6-inch square; set aside. Roll out red dough into a 6x6-inch square, and place on top of plain square. (If dough gets too warm, chill it briefly.) Roll dough gently into a log, wrap in plastic, and chill until firm, about 1 hour.
Heat oven to 350°. Adjust oven racks to upper-middle and lower-middle positions. Line two baking sheets with parchment paper. Cut dough into 1-inch-thick round slices. Place an ovenproof cookie stick inside each cookie. Arrange cookies on baking sheet about 3 inches apart.
Bake until cookies are set, 15-20 minutes total, rotating pans halfway through baking. Transfer pans to wire rack and let cool completely.
Make the icing: In the bowl of a standing mixer fitted with whip attachment, combine remaining 1 cup sugar and egg white on medium speed. Mix in water 1 teaspoon at a time, until mixture is consistency of honey.
Using a small offset spatula, spread icing lightly onto cookies and top with red and white sanding sugars. Let icing set before serving, about 4 hours.