In a large bowl cream butter and sugar until light and fluffy.
Stir in milk, vanilla, and peppermint extract. Stir in cornstarch, cocoa powder, and salt.
Gradually stir in flour a little at a time, mixing until just combined.
Shake dough into 2 logs that are ~ 1 ½ inches in diameter. Wrap in plastic wrap and freeze for 1-2 hours.
Preheat oven to 375 degrees.
Slice dough in ¼ inch thick rounds with sharp knife. Bake for 14-15 minutes. Cool completely.
Grate around 4 ounces of the chocolate bar. Then In a small microwave safe bowl melt the remaining chocolate on high ~20-30 seconds at a time until glossy. Stir in grated chocolate.
Dip each cookie in chocolate, and let set on wax paper for ~1 hour.