Preheat oven to 225 degrees F. Line a large baking sheet with parchment paper; set aside.
Using an electric mixer with the whisk attachment (or a hand mixer), beat the egg whites on medium speed until frothy, then add the cream of tartar, salt, and vanilla extract.
Increase the mixer speed to medium-high and beat to soft peaks. While continuing to beat the egg whites, gradually add the granulated sugar and beat until glossy and stiff peaks form.
Fit a pastry bag with a large star tip (I use the Ateco #827 for an open star, the Ateco #864 for a French star) and fill it with meringue.
Pipe the cookies onto the prepared baking sheet. You do not need to leave much room between the cookies, as they will not spread.
Bake the cookies for 1 hour, or until firm to the touch. Turn the oven off and prop the oven door open with a wooden spoon until the cookies are completely cool. (I usually bake them in the evening and then leave them in the propped-open oven overnight to cool and set up completely.)
Carefully remove from the parchment and store in an airtight container at room temperature, keeping them away from excess heat or moisture (it will cause them to become chewy).