In a small saucepan over medium heat, bring sugar and water to a boil. Continue to boil until sugar syrup reaches 240-244 degrees F, soft ball stage on a candy thermometer. As it cooks, start step 2, the meringue.
While sugar syrup is cooking, separate eggs, placing whites in the bowl of an electric mixer fitted with the whisk attachment. Beat on low to medium speed until foamy. Add cream of tartar, and whip on medium to high speed until stiff peaks form (they should hold their shape when the whisk is lifted).
With the mixer running, add hot cooked syrup to the whites in a slow but steady stream, beating on high speed. Pour into the center of the mixer so that it doesn't touch the mixer bowl; it will harden immediately if it does. Always be careful when working with hot sugar.
Beat on high speed until the bowl is cool to the touch - at least ten minutes.
Switch to the paddle attachment and add butter a tablespoon at a time, beating between additions until you can't see the last tablespoon of butter you added. When you're done adding butter, beat for another 5 minutes.
Beat in vanilla until fully incorporated. The frosting should be smooth, shiny, and hold its shape.
If your frosting turns soupy, the ingredients were probably too hot. Don't worry! Your frosting isn't ruined; refrigerate the mixing bowl for a few minutes and then mix some more - a lot more. Don't give up. Keep mixing and eventually it will come together.Desserts frosted with this frosting can sit at room temperature for up to 3 days.Any leftover frosting can be stored in the fridge for up to one week or frozen for several months. Bring it to room temperature and beat it for a few minutes before using. (If you don't want to save it, you can also bake it into cookies.)