Caramel Frosting

3 cups sugar, divided
¾ cup milk
1 egg, beaten
Pinch of salt
½ cup butter, cut up

Sprinkle ½ cup sugar in a heavy saucepan; place over medium heat.  Cook stirring constantly, until sugar melts and syrup is light golden brown.
Combine remaining 2 ½ cups sugar, milk, beaten egg, and salt, stirring well; stir in butter.  Stir butter mixture into hot caramelized sugar.  (The mixture will tend to lump, becoming smooth with further cooking.)
Cook over medium heat, stirring frequently, until a candy thermometer registers 230° (about 15 to 20 minutes.)  Cool 5 minutes.  Beat with a wooden spoon to almost spreading consistency (about 5 minutes), and spread on cooled cake.  Yield:  about 2 ½ cups.