Preheat oven to 325 degrees. Line two baking sheets with parchment paper and set aside.
Grate one ounce of grated chocolate with a microplane grater, set aside.
In a large bowl, with an electric mixer or stand mixer, whip the egg whites on high speed until light and frothy. Add the sugar and cream of tartar. Continue whipping on high speed until glossy and stiff. Add the peppermint extract and whip just a few more seconds to incorporate the extract into the egg whites. Gently fold the grated chocolate into the egg white mixture.
Scoop the meringue into a pastry bag fitted with a large star tip
Pipe the meringue onto the parchment paper into 1 - 1 1/2 inch stars. Bake for 25-30 minutes until meringues are crispy -- and not soft. Test them by cooling the meringue for a minute, then tasting. They should be crisp all the way through.
Let meringues cool on the pan. Meanwhile, melt the remaining chocolate in the microwave by heating for 10-15 seconds at a time at 50% power. Stir after each interval until chocolate is melted. Do not melt chocolate on high power as it can seize easily. Drizzle melted chocolate on cooled meringues.
Let chocolate harden before transferring to a airtight container to store for up to 3 days.