In a 2- to 3-quart pan over low heat, stir butter and chocolate until melted and blended. Remove from heat and stir in vanilla and 2 cups sugar. Transfer to a bowl. Add 4 eggs, one at a time, beating well after each addition. Stir in flour and baking powder just until blended.
In another bowl, mix fromage blanc and remaining sugar and egg until well blended.
Spread half the chocolate mixture level in a buttered and floured 9-inch square baking pan. Pour cheese mixture evenly over chocolate. Drop 1/4-cup portions of remaining chocolate mixture on top, partially, but not completely, covering cheese mixture.
Bake brownies in a 325° regular or convection oven until a wooden skewer inserted in the center comes out with moist crumbs attached, 45 to 50 minutes. Let cool in pan on a rack for at least 20 minutes, then cut into 9 squares.