Preheat the oven to 200°F.
Put the egg whites, salt, and cream of tartar in the bowl of a stand mixer outfitted with the whisk attachment. Beat at medium speed until the whites turn foamy -- about 90 seconds.
With the mixer running at high speed, add the caster sugar one tablespoon at a time, allowing 15-20 seconds between each subsequent addition. (If you are using regular granulated sugar, add it even more slowly -- just one teaspoon at a time.) Beat in the vanilla extract. Continue beating until the whites turn glossy and hold a stiff peak.
At this point, you can use the batter as is, or beat in droplets of food coloring. My habit is to use half of the batter in its natural hue, and dye the remaining half. Pastel shades of blue, yellow, and pink are great colors for an Easter parade of French Meringue Cookies.
Spoon or pipe the batter onto parchment-lined baking sheets, allowing 1 inch of air space between each cookie. (The cookies for this recipe are approximately 1 1/2 inches in diameter.)
Bake the cookies for 1 hour. Then turn the heat off, but allow the cookies to remain in the oven until they dry completely -- usually 2 hours. If desired, you can leave the cookies overnight in the turned-off oven.