1 Preheat the oven to 200° F and line a baking sheet with parchment paper.
2 Prepare the meringue cookies in a large mixing bowl with a handheld electric mixer, or in a stand mixer with the whisk attachment. Make sure the equipment is free of grease residue and completely dry. Moisture will hinder the egg whites from reaching their full volume potential.
3 Crack the room temperature egg whites (a cold egg white will also hinder the egg white volume) into the bowl, being very careful to not have any yolk, because again, that will hinder the volume.
4 Beat at medium speed for about 1 minute until frothy.
5 Add the cream of tartar (this helps with stabilizing the egg whites). Continue beating at medium speed until the whites become soft peaks. This means the peaks fall over on themselves.
6 Still at medium speed, add the sugar 1 tablespoon at a time, while continuously beating until the whites become stiff peaks. This means the peaks stay upright on their own.
7 When the egg whites look like they have reached stiff peaks, rub a small amount of the meringue in between your fingers, checking for grittiness. If the texture is gritty, the sugar has not completely dissolved and it needs to be beaten for longer until smooth.
8 Add ¼ teaspoon of peppermint extract and beat to combine, and scrape down the sides of the bowl to make sure all the sugar is incorporated and dissolved.
9 With a large star pastry tip, pipe about 144 quarter-sized mounds onto the prepared baking sheet. Evenly distribute the sprinkles on the tops before baking so they will stick.
10 Bake for 45-50 minutes, or until the outsides are crisp and they peel up easily off the parchment.
11 Turn the oven off and crack the door open, and allow the cookies to cool in the oven for 1½ to 2 hours. The outsides will be crisp and the insides will be soft, after cooling completely.
12 If using optional chocolate: When the meringue cookies are completely cool, melt the chocolate according to package directions and dip the bottoms of the cookies in the chocolate. Set them on a silicone baking mat or parchment paper to harden.
13 Store at room temperature for several days.