Preheat oven to 350 degree F. For chocolate batter, in a saucepan melt the unsweetened chocolate and butter over low heat. Remove from heat. Stir in the 1-1/3 cups sugar and 1/2 teaspoon vanilla. Cool 15 minutes. Beat in the 3 eggs and the 3/4 cup flour.
For cheesecake filling, in a mixing bowl combine cream cheese, the 1/3 cup sugar, 1 egg, 4 teaspoons flour, and 1/4 teaspoon vanilla.
Spray an 8x8x2-inch baking pan with nonstick coating. Spread two-thirds of the chocolate batter in the pan. Spoon cheesecake filling over batter. Dollop with remaining chocolate batter.
Bake for 20 minutes. Sprinkle with chocolate pieces. Bake for 12 minutes more. Cool in pan on a wire rack. Cut into squares. Store in an airtight container in the refrigerator. Let stand at room temperature for 30 minutes before serving. Makes 16 bars.