Line an 8-inch square baking pan with heavy-duty foil, leaving a 1-inch overhang on two sides.
In a heavy medium saucepan, combine brown sugar, Marshmallow Fluff, milk, butter and salt and bring to a boil over medium-high heat. Reduce heat to medium and simmer, stirring constantly with a wooden spoon, for 5 minutes. Remove pan from heat, add white chocolate chips and stir until melted. Blend in nuts and vanilla.
Scrape fudge into prepared pan. Refrigerate until firm, 2 to 3 hours. Remove fudge from pan, using foil to lift it out, then cut into 16 cubes; serve. Or chill in an airtight container for up to 1 week.