Line 8- or 9-inch square pan with foil, extending foil over edges of pan. Butter foil.
Mix sugar, cocoa and salt in heavy 4-quart saucepan; stir in milk.
Cook over medium heat, stirring constantly, until mixture comes to full rolling boil.
Boil, without stirring, until mixture reaches 234° on candy thermometer or until small amount of mixture dropped in very cold water, forms a soft ball which flattens when removed from water.
Remove from heat. Add butter and vanilla. DO NOT STIR.
Cool at room temperature to 110°.
Beat with wooden spoon until fudge thickens and just begins to lose some of its gloss.
Quickly spread into prepared pan; cool completely.
Cut into squares. Store in tightly covered contained at room temperature.