Add whites to the bowl of an electric mixer and beat on medium-low for 1-2 minutes.
Add cream of tartar and increase speed to medium. Beat until soft peaks form.
With the mixer still running, slowly begin adding the sugar, about 1 tbs at a time, until all the sugar has been used. Increase the speed to medium-high, then continue beating until stiff peaks form.
Add vanilla, then beat for 30 more seconds.
Either fill a piping bag with the meringue to pipe out cookie shapes, or use a spoon or ice cream scoop to transfer the meringue to the baking sheets.
Bake for 60-90 minutes, depending on the size of the meringues. If you used a spoon or ice cream scoop, they'll take a bit longer. When done, the outside will be crisp, but the inside will feel hollow. Turn off the oven, keeping the door closed, and let the meringues cool. It will take a few hours, but they can stay in overnight.
They'll keep at room temperature in an air tight container for about a week, just don't refrigerate them.