Preheat and Prepare the Pan: Preheat the oven to 350°F. Grease and flour a 9 x 12-inch baking pan.
Melt Chocolate and Butter: Melt the butter and chocolate in a double boiler over boiling water. Once melted, let it cool to room temperature.
Mix Eggs and Sugar: Beat the eggs and sugar together until thick and lemon-colored. Add the vanilla extract.
Combine Ingredients: Fold the cooled chocolate mixture into the egg and sugar mixture. Sift the flour and fold it gently into the batter until just blended. Add the walnuts.
Bake: Pour the batter into the prepared pan and bake for 25 minutes or until the center is just set. Avoid overbaking for a fudgy texture.
Cool and Serve: Let the brownies cool in the pan for 30 minutes before cutting into bars. This recipe makes 28 large brownies.