Line an 8x8-inch baking pan with parchment paper and set aside.

In a heavy-bottomed saucepan, combine sugar, milk, chocolate, corn syrup, and salt over medium heat, stirring constantly until chocolate melts and sugar dissolves.

Attach a candy thermometer to the side of the pan and cook without stirring until the mixture reaches 234-240°F (soft-ball stage), about 10-15 minutes.

Remove from heat and add butter and vanilla without stirring, then let cool undisturbed until the mixture reaches 110°F, about 30-40 minutes.

Beat vigorously with a wooden spoon until the fudge loses its gloss and starts to thicken, about 5-8 minutes.

Quickly spread the fudge into the prepared pan, smoothing the top with a spatula.

Let cool completely at room temperature for at least 2 hours, then cut into 1-inch squares.