In 8- or 10-inch skillet, heat 1/4 cup of the sugar over medium heat until amber colored, about 6 minutes, shaking pan occasionally (do not stir). Meanwhile, in 3-quart saucepan, heat remaining 1 1/4 cups sugar, 1/2 cup butter and the milk to boiling over medium-high heat. Gradually stir in caramelized sugar with whisk; cook and stir to 232°F. Remove from heat; cool to lukewarm, about 20 minutes, stirring occasionally, until frosting is smooth and spreadable. Using offset spatula and working quickly, frost cake (frosting will harden as it cools). Let stand 30 minutes before slicing.