Preheat oven to 350 degrees F. Butter the sides of a 2-quart souffle dish. Sprinkle inside of dish with sugar; set aside.
In a small saucepan cook and stir chocolate over low heat until melted; set aside.
In a small bowl combine the flour and cocoa powder. In a medium saucepan melt the 3 tablespoons butter over medium heat. Stir in flour mixture; gradually stir in half-and-half. Cook and stir over medium heat until thickened and bubbly. Remove from heat. Stir in vanilla. Stir melted chocolate into the hot cream mixture. In a medium bowl beat the egg yolks with a fork just until combined. Gradually stir the chocolate mixture into the egg yolks; set aside.
In a large bowl beat egg whites with an electric mixer on medium to high speed until soft peaks form (tips curl). Gradually add the 1/3 cup sugar, 1 tablespoon at a time, beating until stiff peaks form (tips stand straight).
Gently fold about 1/4 of the the beaten egg whites into the chocolate mixture to lighten. Fold chocolate mixture into remaining egg whites in bowl. Pour chocolate mixture into the prepared souffle dish.
Bake in the preheated oven for 40 to 45 minutes or until a knife inserted near the center comes out clean. Serve souffle immediately. To serve, insert two forks back to back; gently pull souffle apart into six to eight equal-size wedges. Use a spoon to transfer to plates.