Melt chocolate in milk in a heavy saucepan over low heat, stirring constantly. Stir in sugar and salt. Increase heat to medium; bring to a boil, stirring constantly. Continue to boil without stirring until a small amount of the mixture forms a soft ball in cold water, or about 236 F, on a candy thermometer.

Remove the fudge from the heat; add butter and vanilla then cool to lukewarm, or about 110 F.

Beat until fudge loses its gloss, then quickly pour into a pie plate or loaf pan. Cool and cut into squares.