Combine sugar and butter in a 10-inch cast-iron skillet; cook over medium heat, stirring constantly, until sugar dissolves and becomes a golden syrup.
Gradually add warm milk to syrup mixture in skillet, stirring constantly. Continue to cook over medium heat, stirring constantly, until mixture reaches soft ball stage (240°).
Remove from heat; beat at medium speed of electric mixer about 3 to 5 minutes or until thick enough to spread. Spread immediately on cooled cake.