In the bowl of a stand mixer fitted with the whisk attachment, combine the egg whites, cream of tartar, and 1/3 cup sugar. Beat on HIGH speed until stiff peaks, about 6-8 minutes.
In the meantime, combine the water and remaining 1 1/2 cups sugar in a saucepan over medium heat. Use a candy thermometer to heat up to 235F, stirring occasionally.
While the stand mixer is on Medium speed, gradually pout in the sugar syrup. Beat until cool to touch, about 8-10 minutes.
If the meringue is still warm, place in the fridge for 10-30 minutes to cool down.
Switch out the whisk attachment for the paddle attachment. While on Medium speed, gradually add in the cubed softened butter. Beat until a thick and silky meringue buttercream.
TIP: If the mixture seems to thin, place back in the fridge for 20-40 minutes, then beat again until thickened.
Fold in the vanilla extract.