Preheat your oven to 325 degrees. Adjust your oven rack to the middle position. Grease your 8 x 8 square cake pan with cooking spray or butter. Set aside.
In a small saucepan, melt butter, over low heat. Add chocolate and whisk until smooth OR use a small bowl or measuring cup to melt butter and chocolate in your microwave in 20 second intervals, stirring at each interval, until melted and smooth. Set aside to cool slightly.
In a medium to large mixing bowl, whisk dry ingredients (sugar, flour, baking powder, salt).
Mix in the eggs, Kahlua, vanilla, and melted chocolate. Stir until very smooth but not overmixed.
Next, dump your batter into your prepared pan. Do your best to spread the batter as evenly as possible across the bottom of the pan.
Bake until top of brownie begins to crack and a toothpick inserted into the center comes out almost clean. A few crumbs are ok! It will take 35 -42 minutes. Sometimes a little less, sometimes a little more. I always rotate the brownies at about the half way mark.
Once brownies are cooked, remove them from your oven and place on a wire rack to totally cool.