In a heavy-bottomed saucepan, combine 3 cups of sugar with the milk. Place over medium heat, stirring gently for a few minutes to blend the ingredients, then allow the mixture to heat further without stirring.

Meanwhile, in a small black iron skillet, add 5 tablespoons of sugar over medium to medium-high heat. Stir continuously until the sugar melts into a liquid and transforms into a bubbling, golden-brown caramel.

Once the milk and sugar mixture in the saucepan is very hot, carefully pour the caramelized sugar into it. Whisk the mixture thoroughly and cook over medium heat for approximately 15 minutes, or until it reaches the soft-ball stage. Test by letting a small amount of the mixture drop into a glass of cool water; it should form a soft, pliable ball.

Remove the saucepan from heat and immediately incorporate the cold butter using an electric mixer. Beat until the butter is fully blended, and continue mixing as the icing cools and thickens to a spreadable consistency.

If the icing becomes too thick, adjust by beating in milk, one tablespoon at a time, until the desired texture is achieved.

Ensure your cake is completely cooled before applying the icing to prevent cracking.