Preheat your oven to 350°F (175°C). This ensures that your brownies start baking at the right temperature for the perfect fudgy texture.
Grease your 9x13-inch baking pan or line it with parchment paper for easier removal of brownies once baked and cooled.
In a medium saucepan over low heat, combine the butter and unsweetened chocolate. Stir continuously until melted and smooth. Remove from heat and let it cool slightly.
In a mixing bowl, whisk together the flour, baking powder, and salt until well combined. Set aside.
In a large mixing bowl, combine the sugar and eggs. Whisk until the mixture is light and fluffy to incorporate air for a lighter texture.
Pour the slightly cooled chocolate and butter mixture into the egg and sugar mixture. Stir until fully combined.
Add the Kahlua to the chocolate mixture. Stir well to ensure that the coffee flavor is evenly distributed throughout the batter.
Gradually fold the dry ingredients into the wet mixture. Be careful not to overmix; stop as soon as there are no dry spots.
Pour the brownie batter into the prepared baking pan and spread it evenly. Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
Once the brownies are baked and cooled, brush the top with an additional tablespoon of Kahlua for an extra kick of flavor.
Allow the brownies to cool in the pan on a wire rack. Once cooled, slice into squares and serve.