Preheat the oven to 200 degrees and line 2 baking sheets with parchment paper.
Beat the egg whites, vanilla extract, and cream of tartar in a stand mixer with the whisk attachment on medium speed until the mixture is frothy and peaks begin to form.
While the mixer still running, add the sugar one tablespoon at a time, waiting a few seconds between each addition.
After all the sugar has been added, continue beating for around five more minutes, until the mixture is glossy and stiff.
Transfer half the mixture to a piping bag with a large round tip.
Add the red gel food coloring to the remaining mixture and mix until no white streaks appear. Transfer the red mixture to a piping bag fitted with a large star tip.
Pipe a circle of white meringue on each baking sheet and top with a star of red meringue.
Add a small dot of white meringue to the top of the red meringue.
Place the cookies in the preheated oven and bake for 45 minutes. When the cook time is up, turn off the oven and allow the cookies to sit in the oven for an additional 1 hour. Then, remove the pan from the oven and allow the cookies to cool completely before eating or storing in an airtight container.