Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x9 inch baking pan.
In a medium bowl, cream together the sugar and 1 1/2 cups of butter until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Combine the flour and cocoa powder, stir into the creamed mixture until just blended. Spread evenly into the prepared pan.
Bake for 35 to 40 minutes in the preheated oven, until a toothpick inserted into the center comes out clean.
To make the frosting: Combine the semisweet chocolate and remaining 2 tablespoons butter in a small bowl. Heat in the microwave or over a double boiler, stirring frequently until smooth. Spread over brownies when cool.