Wipe down your mixing bowl with vinegar.
Preheat oven to 225F and line a baking sheet with parchment paper. Set aside. Prepare a piping bag with a star tip. Set aside.
Fill a sauce pan with about two inches of water and bring it to a gentle simmer. Separate the yolks from the egg whites and make sure NONE of the yolk gets into your egg white mixture. This could mess up the entire batch. Any fat will prevent stiff peaks from forming. Save the yolks for the lemon curd.
In a heat proof bowl, place the egg whites, sugar, cream of tartar and vanilla extract. Place the bowl on the sauce pan over the simmering water but do NOT let the bottom of the bowl touch the simmering water.
Continuously whisk while the mixture heats up. It will start out thick but will thin out as you keep on whisking. Switch to a rubber spatula and use that to mix (while also scraping the sides of the bowl) for about 4-5 minutes until the mixture is thin and frothy on top - if you have a thermometer, it should be around 160 degrees Fahrenheit.
Use your whisk to pick up some of the mixture and let it drop in between your fingers. If you pinch it together, you shouldn't be able to feel any of the sugar granules.
Remove from the heat. Using a handheld mixer or in the bowl of a stand mixer fitted with the whisk attachment, beat the mixture on high speed for 5-6 minutes until glossy, thick, stiff peaks form. You should be able to turn the bowl completely upside down and none of the meringue will fall out.
Fill your piping bag with the meringue. Pipe cookies onto the baking sheet in any shape you want, although size here is important. Try your best (if you can use a scale, do it) to make each cookie the same size. This is important when it comes to the baking time - you want all cookies to be the same size so that they all cook evenly and fully. See note if you do not have piping materials.
Bake for ABOUT an hour. It could be more - all ovens differ, elevations differ, humidity differs, the size of your meringue differs, etc., so I cannot say how long it will actually take to bake, but you should look for these clues: One. You should be able to gently lift the cookie off of the parchment paper. Two. If you tap the bottom of the cookies with your finger, it should sound hollow. Three. It should also be dry to the touch.
Turn the oven off but leave the cookies on the pan in the oven for one hour with the door shut.
After the hour, crack the oven door open and let them sit in the oven with the door cracked for another hour. This will help to make sure the meringues do not crack.