Preheat oven to 350 degrees. Lightly butter an 8-inch square pan. Line with parchment paper, leaving an overhang on two sides; butter the paper. Set aside.
In a medium saucepan, place butter and cocoa; heat over low, stirring constantly, until butter has melted and mixture is smooth. Remove from heat; stir in sugar, egg, flour, milk, and vanilla until combined.
Spread mixture evenly in prepared pan. Bake until a toothpick inserted in center comes out clean, 25 to 30 minutes. Remove pan from oven; sprinkle top evenly with marshmallows, walnuts, and chocolate chips. Return to oven, and bake until marshmallows puff, about 3 minutes. Cool to room temperature on a wire rack, about 1 hour. Then refrigerate until topping hardens, about 1 hour. Use paper overhang to lift from pan; cut into 12 bars.
Store at room temperature in an airtight container up to 5 days.