Preheat the oven to 350°F. Line one or more baking sheets with parchment paper.
In a medium bowl, whisk together 1 cup all-purpose flour, ½ cup unsweetened cocoa powder, ¼ teaspoon baking powder, and ¼ teaspoon salt. Set aside.
In a large bowl, use an electric mixer to beat 6 tablespoons (¾ stick) unsalted butter (room temperature) and ½ cup granulated sugar until light and fluffy, about 2–3 minutes.
Beat in 1 large egg and ½ teaspoon pure vanilla extract until incorporated.
Gradually add the flour mixture to the butter mixture and mix just until combined; do not overmix.
Using a teaspoon, scoop portions of dough and roll into small balls. Place the balls about 2 inches apart on the prepared parchment-lined baking sheets.
Dip the bottom of a glass in water and flatten each ball into a 1½-inch round about ¼ inch thick.
Bake the cookies for 8–10 minutes, rotating the baking sheet halfway through baking. The cookies should be slightly firm to the touch.
Remove the baking sheets from the oven and let the cookies cool completely on the parchment-lined sheets set on wire racks. Keep the parchment on the baking sheets.
Put 12 ounces chopped bittersweet chocolate, ¼ teaspoon peppermint extract, and 1⁄6 teaspoon salt in a microwave-safe bowl. Microwave in 30-second intervals, stirring after each interval, until the chocolate is smooth. (Alternatively, melt the chocolate in a heatproof bowl set over a pan of simmering water, stirring until smooth.)
Working with cooled cookies, set a cookie across the tines of a fork and dip the top into the melted chocolate. Tap the underside of the fork on the side of the bowl to remove excess chocolate and create a smooth top.
Gently transfer each dipped cookie back onto the parchment-lined baking sheet. Decorate with sprinkles or nonpareils, if desired.
Refrigerate the baking sheet until the chocolate is firm, about 30 minutes. Keep the cookies chilled until ready to serve.