Preheat oven to 350 degrees F (175 degrees C). Grease and flour an 8-inch square pan.
In a large saucepan, melt 1/2 cup butter. Remove from heat, and stir in 1 cup white sugar, 2 eggs, and 1 teaspoon vanilla. Beat in 1/3 cup cocoa, 1/2 cup flour, 1/4 teaspoon salt, and 1/4 teaspoon baking powder. Spread batter into prepared pan.
Bake for 25 to 30 minutes in the preheated oven. Do not overcook.