Butter an 8 x 8-inch square pan. Combine the sugar, butter, milk, salt and chocolate in a saucepan. Cook, stirring constantly, over medium heat, until all ingredients melt and come to a boil, 15 to 20 minutes.
Insert candy thermometer and let boil slowly without stirring for about 25 minutes to soft-ball stage (238 degrees F on a candy thermometer).
Remove saucepan from heat; let cool for 10 minutes. Beat in vanilla with electric mixer at medium speed for 2 to 3 minutes or until fudge loses its gloss.
With rubber spatula, fold in nuts until evenly distributed. Scrape into jelly-roll pan; spread to edges. Cool at room temperature 40 minutes or until firm. Cut into 36 squares. Store in airtight container or wrap in foil. Makes 36 squares.