Pour egg whites into the bowl of a stand mixer fitted with a whisk attachment; beat on low speed until foamy. Add cream of tartar, increase speed to medium-high, and beat until stiff peaks form.

Combine sugar and water in a small saucepan over medium heat; bring to a boil. Cook until syrup reads 240 degrees F (115 degrees C) on a candy thermometer or until a small amount of syrup dropped into cold water forms a soft ball that flattens when placed on a flat surface.

Increase mixer speed to high and pour syrup in a slow and steady stream down the side of the bowl, beating until meringue is no longer steaming, 2 to 3 minutes. Beat in butter one cube at a time until buttercream reaches a soft and spreadable consistency, 3 to 5 minutes. Beat in vanilla extract.