Lightly brush an 8-inch baking dish with butter, then line with parchment paper, leaving a 2-inch overhang on both sides. Lightly butter the parchment paper.
In a medium saucepan, combine the remaining 2 tablespoons of butter, sugar, evaporated milk and salt. Bring to a boil over medium-high heat, stirring constantly, then cook for another 3 minutes, until golden and slightly thickened. Remove from heat and stir in marshmallows until almost melted, then add chocolate and vanilla. Stir until chocolate and marshmallows are completely melted and mixture is smooth. Pour into prepared pan over smooth top with spatula.
Refrigerate until firm, at least 2 hours. Remove parchment paper with fudge from pan and cut into 36 squares. Fudge can be stored in the refrigerator, covered with plastic, for up to 1 week.
