1. Heat oven to 350 degrees F.
2. Heat together butter and 3 ounces (about 1/2 cup) bittersweet chocolate in medium-size saucepan over medium-low heat, stirring, until butter and chocolate are nearly melted. Remove saucepan from heat; stir until mixture is completely melted. Stir in the 1/2 cup sugar. Working quickly to prevent curdling, whisk in 1 of the eggs. Stir in the flour to make a smooth batter. Spread the batter evenly over the bottom of an ungreased 9 x 9 x 2-inch square baking pan. Place the baking pan in the refrigerator while proceeding with Step 3.
3. In the same saucepan, combine the heavy cream and the remaining 1/3 cup sugar. Bring to boiling over medium-high heat. Meanwhile, place the remaining 6 ounces (about 1 cup) of bittersweet chocolate in a small bowl. Pour the hot cream mixture over the chocolate in the bowl; let stand for 2 minutes. Then stir the mixture until the chocolate is melted and smooth. Whisk in the remaining 2 eggs until the mixture is smooth. Spread chocolate mixture evenly over the batter in the pan.
4. Bake in 350 degree F oven until the top center of the cake is soft but no longer liquid, 26 to 30 minutes. Let cool in pan on wire rack at least 10 minutes. Then cut into bars or diamonds. (Bars can be refrigerated, covered, for up to 5 days, or frozen up to 1 month.) Serve slightly warm, chilled or at room temperature. Decorate with melted white chocolate, if desired.Makes 24 bars or diamonds.Note:
5. To melt white chocolate, microwave in small bowl on high for 1 minute. Stir until smooth. Scrape into small plastic food-storage bag. Snip a small corner; drizzle over brownies. Let stand until firm.