Preheat oven to 220F. Cover two large baking sheets with parchment paper.
Separate the egg whites into a large mixing bowl (you can save the yolks for something else).
Add the cream of tartar to the eggs.
Beat the eggs on medium using a hand or stand mixer with whisk attachment until you have soft peaks (the mixture will be light and fluffy, but when you take the whisk out of the bowl, it'll collapse back onto itself).
At that point, start adding the sugar in, about a tablespoon at a time. Beat on high. Don't rush this process. It takes me about 8-10 minutes to use it all up. Once the sugar is completely dissolved (rub some between two fingers, if it feels gritty, keep beating the meringue), you should have a glossy meringue that holds stiff peaks (take the whisk out of the bowl and the meringue's shape will hold). Add the vanilla and almond extracts, and beat until they're well mixed in.
Fold the top third of your piping bag inside out and paint your food coloring stripes inside the bag (from the fold all the way to the piping tip). Spoon the meringue in (fill bag about 3/4 full), unfold the top and twist it, then squeeze a bit of the meringue out (discard it) to get any air bubbles out. Pipe onto the parchment-lined baking sheets, keeping in mind the meringue expands while it cooks, so leave a decent gap between each cookie.
Bake for 1.5 hours. Turn the oven off and let the meringues sit in the oven for at least an hour to help them dry out even more (and prevent too much cracking), then finish cooling them on a cooling rack. You can even leave them in the oven to cool off overnight.
Store in an airtight container. They will keep for about a week.