1. Preheat oven to 350 degrees. In a medium bowl, whisk together flour, cocoa, baking powder, and 1/4 teaspoon salt. Set aside.

2. Using an electric mixer, beat butter and sugar until light and fluffy. Beat in egg and vanilla. With mixer on low, gradually add flour mixture; mix just until combined.

3. Form balls of dough (each equal to 1 teaspoon), and place on 2 baking sheets, about 2 inches apart. Dip the bottom of a glass in water, and flatten balls into 1 1/2-inch rounds (about 1/4 inch thick). Bake until slightly firm to the touch, 8 to 10 minutes, rotating sheets halfway through. Immediately transfer cookies to a wire rack to cool completely.

4. Make chocolate coating: Place chocolate, peppermint extract, and remaining 1/8 teaspoon salt in a large heatproof bowl set over (not in) a saucepan of simmering water. Heat, stirring occasionally, until smooth, 2 to 3 minutes; remove from heat.

5. Line a baking sheet with parchment or waxed paper. Set each cookie across the tines of a fork, dunk in chocolate, then tap underside of fork on side of the bowl to allow excess chocolate to drip off. Place cookies on prepared baking sheet, and decorate with sprinkles, if desired. Refrigerate until chocolate has hardened, about 30 minutes, and keep chilled until ready to serve.