Butter 8- or 9-inch square pan; set aside.
Combine 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, to soft-ball stage, 234°F on a candy thermometer (or until syrup, when dropped into very cold water, forms a soft ball that flattens when removed from water).
Bulb of candy thermometer should not rest on bottom of saucepan.
Remove from heat.
Add butter and vanilla; do not stir.
Cool at room temperature to 110°F (lukewarm).
Beat until fudge thickens and loses some of its gloss.
Quickly spread in prepared pan; cool.
Cut into 1- to 1 1/2-inch squares.