Preheat your oven to 350 degrees F and line an 8x8in baking pan with parchment paper, leaving enough overhang for easy release later on. Spray with a nonstick spray and set aside.
Add the butter to a medium skillet over medium-low heat. Melt the butter and continue to cook until the butter is bubbly and brown bits have started to form on the bottom of the pan. Remove from heat immediately to keep from burning and transfer the butter to a large bowl.
Melt the chocolate in the microwave in 25 second increments until completely melted, stirring after each increment (it took me 1 minute total to melt the chocolate). Add to the large bowl with the brown butter.
To the bowl, whisk in the sugars until smooth and creamy. Add each egg, one at a time, whisking after each addition. Whisk in the bourbon, vanilla and salt. Fold in the flour until just moistened and pour into the prepared baking pan. Smooth out the top with an offset spatula.
Bake the brownies for 25-30 minutes or until a toothpick comes out clean. Remove from heat and allow to cool completely at room temperature.
While the brownies are cooling, prepare your frosting. Melt the chocolate in the microwave in 25 second increments until completely melted, stirring after each increment (it took me 1 minute total to melt the chocolate). Add it to the bowl of a stand mixer, with paddle attachment fixed. Add the cream cheese also to the bowl. Mix until smooth. Add the confectioner's sugar in 1/2 cup increments with the mixer speed set on low until all has been added. Add the salt and the milk and mix again. The frosting should be fairly thick, but if it is still too thick to spread, add more milk to reach this consistency.
Spread the frosting on the cooled brownies and cover with foil. Place the brownies in the fridge for 30 minutes before releasing them from the pan and slicing them.
Store in an airtight container for 3-4 days. Enjoy!