Start by preheating your oven to 350 degrees Fahrenheit.
Grease your 8x8 cake pan with butter and cut two 8-inch wide rectangles of parchment paper to line the pan (the rectangles will overlap in the middle). It's important to grease the pan before adding the parchment paper. This helps the parchment stick and line the pan smoothly. Lining the pan with parchment allows you to lift the cake out easily after baking and it also ensures that no part of the cake gets stuck to the pan during baking.
Melt the butter in a saucepan on the stove or in the microwave and pour it into a mixing bowl.
Add the brown sugar, vanilla extract, and cocoa powder. Mix well until everything is combined and then stir in the egg until it is completely incorporated.
Add the flour, baking powder and salt. Mix the dry ingredients in just until combined. Over mixing can cause the cake to be too flat, dense and dry instead of moist and chewy.
You'll have a thick batter that doesn't pour into the pan very easily, but don't panic. Spread the mixture into the corners as best you can using an offset spatula or a knife. Don't worry if the mixture still doesn't hit the side of the pan.
Bake for 23-25 minutes (at 350 degrees).
While the cake is baking, prepare the frosting since you're going to frost the cake soon after it comes out of the oven (while it's still very warm).
Add 2 tbsp softened butter to a small mixing bowl and add the icing sugar, 1 tbsp cocoa powder and milk. Stir the frosting ingredients together using a spoon until it has reached a spreadable consistency.
When you remove the brownies from the oven after baking, let them cool for only about 5-10 minutes before you frost. It's ideal if they're very warm but not hot when you spread the frosting.
Feel free to add chopped nuts to the top if you wish, but we love to enjoy these just as they are!
Cut the brownies into 9 perfectly-sized squares and serve!