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 walnuts until well blended.
Spread batter evenly in a buttered and floured 8-inch square baking pan.
Bake in a 350° oven until edges feel firm to touch and begin to turn a shade darker, 25 to 30 minutes.
Run a knife between pan rim and brownie. If desired, spread with chocolate glaze. Let cool in pan on a rack, about 1 hour. Cut into 9 or 16 squares.
Chocolate glaze. In a 1- to 2-quart pan over low heat, frequently stir 1/3 cup whipping cream and 1 cup (6 oz.) semisweet chocolate chips until melted and smooth. Stir in 1 teaspoon vanilla. Use warm.
Note: Nutritional analysis is per small brownie.