Line an 8x8-inch baking pan with parchment paper and grease lightly with butter. Set aside.

Whisk together the sugar, cocoa powder, and salt in a 3-quart heavy-bottomed saucepan until no cocoa lumps remain.

Pour in the milk and stir to combine, then place the pan over medium heat.

Stir continuously until the sugar dissolves and the mixture comes to a full boil, about 5 to 7 minutes.

Once boiling, stop stirring. Clip the candy thermometer to the side of the pan so the tip is submerged but not touching the bottom.

Cook at a steady boil, without stirring, until the thermometer reads 238 F (114 C), the soft-ball stage. This takes about 10 to 15 minutes depending on your stove.

Remove the pan from the heat. Add the butter pieces and vanilla extract but do not stir yet.

Let the mixture cool undisturbed until the temperature drops to 110 F (43 C), about 30 to 40 minutes. The pan will feel warm but not hot to the touch.

Once cooled to 110 F, beat the fudge vigorously with a wooden spoon, stirring in wide circles, until it loses its gloss and starts to look matte and thick. This takes 5 to 10 minutes of steady beating.

Working quickly, pour and scrape the fudge into the prepared pan and spread it into an even layer with a spatula.

Let the fudge set at room temperature for at least 2 hours until firm. Cut into 1-inch squares with a sharp knife.