Prepare an 8- or 9-inch square pan by lining it with foil. Grease the foil generously with butter.
Stir sugar, cocoa powder, and salt together in a large, heavy pot over medium heat. Combine well.
Stir in the milk with a wooden spoon. Bring the milk to a full boil, stirring constantly. Bring it to a boil without stirring until a candy thermometer reads 234 degrees F.
Turn off the heat and remove the pan. Stir the butter and vanilla into the saucepan until the temperature reaches 110-120 degrees F, but do not stir.
Beat the fudge with the wooden spoon once it has cooled so that it has thickened and lost some of its glossiness.
Put the fudge in a greased pan and spread it quickly. Allow to cool slowly.
Once completely cooled, cut into squares. Wrap the fudge loosely in foil and store it in the refrigerator.