Combine the milk, butter, salt, brown sugar, granulated sugar, and dark chocolate in a 3-quart saucepan.

Heat the mixture over medium heat, stirring continuously with a fork until the chocolate melts and the syrup starts bubbling around the edges, approximately 8 minutes.

To prevent sugar crystals, use a pastry brush dipped in water to clean any residue from the sides of the pan. Reapply water as needed for a smooth result.

Attach a thermometer to the saucepan and cook the mixture without stirring until the temperature reaches 240°F. This step takes about 5 minutes, and you will notice vigorous bubbling during this process.

Remove the saucepan from heat and allow the mixture to cool undisturbed until it reaches 118°F, which takes roughly 1½ hours. Some chocolate flecks around the edges are normal at this stage.

Lightly grease a 12-inch square surface and prepare parchment paper to use for shaping and rolling.

Once the syrup has cooled, stir in the vanilla extract using a flexible spatula. The mixture may initially feel gritty, but this will smooth out as you continue.

Begin kneading the mixture on the prepared surface, folding and spreading it into a ½-inch thick layer. Use a bench scraper to fold the fudge back into a lump repeatedly until it becomes glossy and smooth, about 5 minutes.

Lay parchment paper over the kneaded fudge and roll it out into a 9x12-inch rectangle that is about ½ inch thick.

Cut the fudge into 48 squares and store them in an airtight container, separating each layer with parchment paper. The fudge will keep for up to 3 weeks at room temperature or up to 2 months if refrigerated.