Preheat oven to 200°F. Mix ingredients and blend with a hand mixer on medium speed until it forms stiff peaks, about 10 minutes. Line a cookie sheet with parchment paper. Using two spoons, scoop up some of the mixture with one spoon and use the other spoon to slide it onto the parchment paper. Leave a little bit of room around each cookie, they don't need much.
Put cookie sheet into oven, let bake for 2 hours and then turn the oven off. If you have the time, let it sit in the oven for at least one more hour to continue drying. They can be left in the oven (assuming it's turned off!) overnight.
The amounts above are just the proportions. Scale it up to however many egg whites you have. I usually have three egg whites from making ice cream, so I use 3 whites, 3/4 cups sugar, 3/8 tsp cream of tartar and 3/8 tsp vanilla.
After they've cooked, you can put them into a ziplock bag and keep them for several weeks.
I started making meringue cookies to use up the leftover whites when making ice cream. If I'm making ice cream, I make these while the cream and milk mixture is simmering.
Any yolk at all in the mix, and they won't whip up. I crack the eggs one at a time, pull the yolk out, and then put the white into the bowl to be whipped. If the yolk breaks, and I'm making ice cream, I just put that white into the ice cream.