Place the butter, powdered sugar, vanilla and peppermint extracts and salt in the bowl of a stand mixer, or in a large mixing bowl if using a hand mixer.
Beat on medium speed until smooth, about 4 minutes. Turn mixer to low and gradually add flour, and then peppermint candies. Mix until a dough forms.
Pat the dough into a ball, and then form into a log shape - approximately 2-inches in diameter, by 16 inches long.
Wrap the log in plastic wrap, and refrigerate until firm, about 2 hours or overnight.
Preheat the oven to 325 degrees
Line a cookie sheet with parchment paper or a Silpat baking mat
Remove the dough from the refrigerator, and slice into ½-inch thick slices.
Place on prepared cookie sheet, at least 1-inch apart. Bake for about 15 minutes, or until the bottoms just start to turn golden. Check them after 10 minutes, as ovens can vary!
Let cool for about 5 minutes before removing from the tray.
Melt the chocolate in a glass bowl or measuring cup, in the microwave, about 30-45 seconds.
Drizzle chocolate over the cooled cookies, and let set at room temperature.
Store cookies in a covered container in the freezer.