Preheat the oven to 175°C. Grease and flour an 8-inch square or loaf pan.
Melt the ½ cup butter in a large saucepan. Remove from heat, and stir in sugar, eggs, and 1 teaspoon vanilla. Beat in the ⅓ cup cocoa, flour, salt, and baking powder. Spread batter into prepared pan.
Bake in the preheated oven until top is dry and edges have started to pull away from the sides of the pan, about 25-30 minutes. Let cool briefly before frosting.
To make the chocolate frosting: Combine the softened butter, icing sugar, 3 tablespoons cocoa, honey, and 1 teaspoon vanilla extract in a bowl. Stir until smooth. Frost brownies while they are still warm.