Preheat the oven to 275F °F (135 °C) and line two baking sheets with parchment paper or silpats.
To the bowl of a stand mixer fitted with the paddle attachment, add the egg whites and beat at medium-low until the egg whites are frothy. This takes about 30 seconds.
Add the cream of tartar and continue mixing at medium-low speed until combined.
Gradually add the granulated sugar, about a tablespoon at a time. It should take 1-2 minutes to add all of the sugar.
Once all of the sugar has been fully incorporated, turn the mixer to medium speed. Beat the mixture until stiff peaks form, which will take about 3 minutes.
Mix in the peppermint extract just until combined.
If you want to make a candy cane design, use a small spoon or a food brush to paint four vertical lines on the inside of a disposable piping bag which has been fitted with a round or star tip. If you would like small red accents around the edges, paint four ¼-inch thick lines. If you want the meringues to be red and white like candy canes, paint four 1-inch thick lines.
Carefully fill the bag with meringue. Try not to smudge your food coloring lines. If it happens, don’t worry. They’ll still come out nicely.
Pipe 1” meringues onto the prepared baking sheet, leaving at least 1” space between them.
Sprinkle the sprinkles over the top, if using.
Bake the meringues for 60-65 minutes or until they’re dry and crisp. Turn off the oven, open the oven door, and let the meringues cool to room temperature. This will take about an hour.
Store meringues in an airtight container for up to 5 days.