Old-Fashioned Fudge Icing (Vintage Cooked Frosting)

Instructions

Combine the dry ingredients. In a medium, heavy pot — such as cast iron or a thick-bottomed saucepan to ensure even heating — whisk together the sugar, cocoa, and salt until the mixture is well blended and free of clumps. This helps the cocoa disperse smoothly once the liquid is added.
Add the milk and butter. Switch to a wooden spoon and gradually stir in the milk. Add the stick of butter to the pot. As the butter melts, it will help the mixture combine evenly and prevent the cocoa from sticking to the bottom.
Bring to a rapid boil. Cook the mixture over medium heat until it reaches a full, rolling boil that cannot be stirred down. This stage is important — the boil should be constant and active. Once it reaches that point, begin timing.
Boil exactly 3 minutes and 45 seconds. Keep the mixture at that steady boil for the full time, stirring constantly. This precise timing helps the icing achieve the proper consistency so it will thicken correctly when beaten.
Add the vanilla. Once the cooking time is complete, remove the pot from the heat and immediately stir in the vanilla extract. Adding it last preserves its flavor and aroma, which would diminish if cooked too long.
Cool briefly. Allow the mixture to cool for no more than 5 minutes. Cooling too long will make the icing stiff too quickly, but a short rest helps bring the temperature down just enough for beating.