Combine the sugar and butter in a 10 inch cast iron skillet (you will be cooking and beating the frosting in the same pan). Cook over medium heat until the sugar dissolves, stirring constantly. The mixture will turn a golden color.
Once the color is golden, gradually stream in the warmed milk stirring constantly. The mixture will bubble. Attach a candy thermometer to the pan and continue to cook, stirring constantly, until the mixture is bubbling with a golden brown color and the temperature is 240 degrees F.
Remove from heat, and place on a towel lined heat proof counter. Using a hand mixer, beat the frosting about 5 minutes or until it is thick enough to spread on a cake.
Spread frosting between layers of cake, and tops and sides. Allow the frosting to set before serving.