Preheat the oven to 200 degrees. Line your cookie sheet with parchment paper and set aside.
If you want to add your stripes to the cookies, prepare a piping bag by painting thin stripes of red food coloring down the side. Make sure that your preferred tip is already attached, then store the piping bag standing upright in a drinking glass or vase until you're ready for it. If you don't want the stripes, just get the piping bag prepared with the coupler and tip.
Beat the egg whites on low / medium-low speed until they become foamy.
Add cream of tartar to the egg whites and continue to beat, increasing speed to medium. Beat until the egg whites begin to turn fluffy.
Gradually add the sugar - very gradually. About a tablespoon at a time, and make sure you are still beating the eggs at the same time.
After all the sugar has been added, turn the speed up to high and add in the peppermint extract. Beat until glossy and stiff peaks form -- about 5 - 7 minutes.
Carefully spoon the meringue into your prepared piping bag. If you're using the stripes, it will take a few squeezes before you'll be able to see them.
Pipe bite-size cookies onto the parchment paper lined cookies sheets.
Bake for one hour at 200 degrees, then turn off the oven but do not remove the cookies.
Leave the cookies in the oven until it has finished cooling. This helps the cookies to completely dry out. If you piped larger cookies, you may want to leave them in the oven overnight. For small cookies, an hour or two should suffice.
When the cookies are done and completely dry, line another cookies sheet with wax paper. Melt the chocolate either in the microwave or in a double boiler.
When the chocolate is smooth, gently begin dipping the meringues in and place them on the wax paper lined cookie sheet.
Set the cookies aside at room temperature until the chocolate sets.