In a small saucepan, combine sugar and ⅓ cup (80 grams) water. Bring to a boil over high heat, being careful not to splash sides of pan, stirring to help sugar dissolve. (Do not stir once mixture starts to boil.) Cook until an instant-read thermometer registers 240°F (116°C).
Meanwhile, in the bowl of a stand mixer fitted with the whisk attachment, beat egg whites and cream of tartar at medium speed until soft peaks form.
With mixer on medium speed, pour hot sugar syrup between side of bowl and whisk attachment in a slow, steady stream. Increase mixer speed to high, and beat until bowl is cool to the touch, 4 to 5 minutes. Beat in vanilla. Use immediately.