Combine corn syrup, 1/2 cup plus 2 tablespoons sugar, and 1/4 cup water in a small saucepan over medium-high heat. Bring to a boil, stirring just until sugar dissolves. Cook, without stirring, 4 minutes or until a candy thermometer registers 240°.
Combine egg whites and cream of tartar in a large bowl; beat at high speed with an electric mixer until foamy. Gradually add remaining 2 tablespoons sugar; beat at high speed until medium peaks form. Gradually pour hot sugar mixture into egg white mixture, beating first at medium speed and then at high speed until stiff peaks form. Stir in vanilla.