Butter an 8x8-inch pan well and set it aside. Have the butter and vanilla measured and waiting by the stove — once the fudge is ready to beat, there is no time to go looking.

In a heavy 3-quart saucepan (the mixture will bubble up), whisk together the sugar, cocoa and salt until no cocoa lumps remain. Stir in the milk until smooth.

Cook over medium heat, stirring constantly, until the mixture comes to a full boil. Then stop stirring, clip on a candy thermometer, and let it boil gently, undisturbed, until it reaches 234°F (soft-ball stage), about 15–20 minutes.

Take the pan off the heat. Drop in the butter and vanilla — do not stir them in. Let the fudge cool undisturbed until the thermometer reads 110°F, about 30 minutes. Walk away; stirring now is how fudge turns grainy.

Beat the fudge with a sturdy wooden spoon until it thickens, loses its glossy shine and starts to hold its shape, about 5–10 minutes of steady beating. It will go from shiny and pourable to dull and heavy — that change is the sign to move fast.

Quickly scrape the fudge into the buttered pan and spread it to the corners before it sets. Let it stand at room temperature about 2 hours, until firm.

Cut into 36 small squares (6 by 6) with a sharp knife, wiping the blade between cuts for clean edges.