In a saucepan, melt the unsweetened chocolate and butter over low heat. Remove the mixture from the heat.Stir in 1-1/3 cups of the sugar and the 1/2 teaspoon vanilla. Cool the mixture for 15 minutes. Beat in the 3 eggs and the 3/4 cup flour.
In a mixing bowl, mix the remaining 1/3 cup sugar, the cream cheese, the 1 egg, the 4 teaspoons flour, and the 1/4 teaspoon vanilla.
Coat an 8x8x2-inch baking pan with nonstick cooking spray. Spread 2/3 of the chocolate batter in the pan. Spoon cream cheese layer over batter. Dollop with remaining chocolate batter.
Bake in a 350 degree F oven for 20 minutes. Sprinkle with chocolate pieces. Bake for 12 minutes more. Cool. Cover; store in the refrigerator. Let the chilled dessert stand at room temperature for 30 minutes to serve. Makes 16 servings.