Pre-heat oven to 350°F (180°C) with rack in the middle position.
Prepare the cake tin: Butter the tin, sides and all. Press a 9" square (23cm) of parchment paper into the tin and butter that too.
Resift the flour with the baking powder and salt into a small bowl or on to a sheet of waxed (grease proof) or parchment paper.
In a medium bowl melt the butter and chocolate over a pan of barely simmering - not boiling - water. Do not let the bowl come into contact with the hot water! Stir occasionally until completely melted, smooth and glossy. Remove the bowl from the heat.
In a large bowl with an electric mixer (or in the work bowl of a KitchenAid mixer) whisk together the sugar and eggs until light and aerated.
With a rubber spatula stir in the melted chocolate and the Kahlúa until well mixed. Fold in the flour mixture until there are no traces of raw flour visible.
Stir in the optional walnuts.
Pour the batter into the prepared cake tin and bake for 30-35 minutes or until the brownies look like they are about to separate from the sides of the tin. Check frequently towards the end of the bake time and take care not to over bake.
Remove the brownies from the oven and cool completely before brushing the top with the optional tablespoon of Kahlúa.
Once cooled, run a small metal spatula around the edges to make sure the brownies don't stick. Place a cooling rack over the tin and invert the brownies which should drop right out. Place a cutting board over the brownies and invert it again, right side up and cut into 16 2-1/4" (6cm) squares.