Heat oven to 350°F and arrange a rack in the middle. Grease a 9 x 13-inch baking pan and line with parchment paper, leaving an overhang on the sides to lift the finished brownies out (makes cutting easier!). Set aside.
Combine 1 cup chocolate chips, 12 tablespoons butter, and 4 ounces chopped unsweetened chocolate in a heatproof medium bowl and place over a saucepan of barely simmering water. Make sure the bottom of the bowl is not touching the water. Heat until chocolate is melted and smooth, stirring occasionally. Remove from heat and let cool slightly. This can also be done in a microwave, melting in 30-second increments, whisking after each, until completely smooth.
Meanwhile, combine 1 cup flour, 2 teaspoons espresso powder, and 1/2 teaspoon salt in a medium bowl. Whisk to combine.
In a separate large bowl beat the 4 eggs until smooth. Add the 1 cup sugar and whisk until eggs are pale in color and thickened slightly. Add cooled chocolate and 1/2 cup Kahlúa and whisk until smooth. Add the flour mixture and stir until just incorporated. Fold in the 1/2 cup cappuccino chips, if using.
Pour into the prepared pan and smooth the top. Bake 35-40 minutes or until a toothpick inserted in the center comes out with moist crumbs attached. Cool in the pan completely before cutting or frosting.
For the frosting: In a small saucepan, bring the 1/2 cup Kahlúa to a boil over medium-high heat. Once boiling, reduce to medium heat and allow to simmer until reduced down to 1/4 cup about 5 minutes. Set aside to cool for at least 10 minutes.
In a large bowl using a handheld or stand mixer fitted with a whisk attachment, beat the 2 sticks of butter on high speed until completely smooth and creamy, about 2–3 minutes. Add the 4 cups powdered sugar, beating on low at first then increasing to high speed.
Once creamy and combined, beat in 1/4 cup of reduced Kahlúa, the espresso powder, vanilla extract, and salt.
When cool, lift the brownies out by gripping the parchment overhangs and transfer to a cutting board. Spread frosting over cooled brownies. Use a sharp knife to cut into squares.
Cover and store leftover brownies in the fridge for up to 1 week.