Preheat the oven to 200°F.

Line two baking sheets with parchment paper and set aside.

Combine the egg whites and cream of tartar in a large mixing bowl and whip on high speed until frothy, 20-30 seconds. Continue to beat on high speed, gradually adding the sugar over 1-1 1/2 minutes until all has been added. Scrape down the sides of the bowl and add the vanilla and peppermint extracts. Whip whites on high speed, stopping to scrape the bowl once or twice, until stiff, glossy peaks form when the whisk is lifted from meringue, 4-5 minutes total.

Turn a piping bag inside-out. Using a paintbrush, make 4-6 lines with the red food coloring up the sides of the bags, starting from about 1 inch above the tip and ending about 3 inches below the top edge of the bag. Carefully turn the bag right-side-out, and place tip-side-down in a tall glass. Fold the unpainted cuff over the edge of the glass. Using a rubber spatula, spoon half of the meringue into the prepared piping bag. Repeat with a second bag and the remaining meringue.

Unfold the cuffs of bags and twist closed at the top. Snip a 1-inch tip off each bag. Holding the piping bag straight above the prepared baking sheets, gently squeeze from the top to form meringue "kisses" about 1 inch tall and 1 1/2 inches wide. Space the meringues about 1 inch apart on the baking sheets.

Bake the meringues on racks in upper third and lower third of oven for 30 minutes. Switch pan positions, then continue baking until meringues feel firm and dry when lightly pressed, 30-40 minutes. (Pro Tip: Depending on your oven and the level of humidity in your area, the meringues may need an additional 5-15 minutes beyond the second bake time to reach the proper level of doneness.)

Check to see that meringues are done. Add time as needed, and when done, turn off oven and allow meringues to rest inside for one hour to crisp the centers. If you prefer a slightly chewy center, skip this step and remove the meringues from the oven immediately.

Transfer pans to cooling racks to cool completely, about 30 minutes.

Serve meringues immediately, or store in an airtight container at room temperature for up to 1 week.