Adjust the oven racks to upper and lower-middle positions. Preheat to 225 F. Line 2 large baking sheets with parchment paper.
Add the egg whites and cream of tartar to the bowl of your GE Stand Mixer fitted with the whisk attachment. Make sure the bowl is clean. Beat the egg whites on medium speed until they look frothy (about 2-3 minutes.)
Increase the speed to medium-high and add the sugar one tablespoon at a time. Once all the sugar is added, turn the speed all the way up to high and beat the egg whites until they are glossy and form stiff peaks when the beater is lifted, about 4 minutes.
Turn the speed down to low and slowly add in the peppermint extract. Mix until combined, about 1 minute, then turn off mixer.
Use a small brush to paint lines of red food coloring inside a piping bag fitting with a large piping tip, spacing the lines ½ to 1-inch apart.
Fill the bag with meringue and pipe cookies on to the prepared baking sheets, spacing them about an inch apart.
Bake the meringues for 1 hour, turn the oven off, and leave the meringues in the oven for another hour. Do not open the door. Test the meringues after 1 hour. If the centers are still chewy, let them dry for a couple more hours.
Make ahead tip
Meringues will keep for several weeks stored in an airtight container either at room temperature, in the refrigerator, or in the freezer. Just make sure the container seals tightly!