In a 2- to 3-quart pan over low heat, frequently stir butter and chocolate until melted and smooth. Remove from heat and stir in sugar, eggs, vanilla, flour, and marshmallows until well blended.
Spread batter evenly in a buttered and floured 8-inch square baking pan. Sprinkle top evenly with walnuts.
Bake in a 350° oven until deep brown, 30 to 35 minutes.
Run a knife between pan rim and brownie. Let cool in pan on a rack, about 1 hour. Cut into 9 or 16 squares.
Notes: Nutritional analysis is per small brownie. Store brownies airtight for up to 2 days.