Preheat oven to 200 degrees. Line two baking sheets with parchment paper and set aside.
In a large bowl, with an electric mixer or stand mixer, whip the egg whites on high speed until light and frothy. Slowly 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 1-1½ inch stars. Bake for 2-3 hours 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.
Transfer to an airtight container and store for up to 3 days.