In a small saucepan over medium heat, bring sugar and water to a boil. Clip a candy thermometer onto the saucepan. Boil the syrup, brushing down the sides of the pan with a pastry brush dipped in water to prevent crystallization, until the syrup registers 240 degrees (soft-ball stage).
In the bowl of an electric mixer fitted with the whisk attachment, beat egg whites on low speed until foamy. Add cream of tartar, and beat on medium high until stiff but not dry peaks form.
With the mixer running, pour the sugar syrup down the side of the bowl (to prevent splattering) into the egg whites in a steady stream, and beat on high speed until the steam is no longer visible, about 3 minutes. Beat in butter, piece by piece. Add vanilla; beat until smooth and spreadable, 3 to 5 minutes. If it looks curdled at any point during the beating process, continue beating until smooth.