Preheat oven to 350F.
Spray a 9x13" pan with cooking spray and then cut parchment paper for the bottom. Spray the paper once it's inserted in the pan.
Combine the butter and unsweetened chocolate in a large saucepan and heat on medium until both are melted. Stir often and watch carefully.
Remove from the heat and whisk in cocoa, sugar, and salt (mixture will be grainy - keep going). Add the beaten eggs and vanilla; combine well and then beat in the beer.
Whisk in the flour just until fully incorporated then stir in the chocolate and white chocolate chips.
Spread the batter into the pan and bake for 25-30 minutes or until a toothpick inserted in the center comes out clean. Cool completely.
Once the brownies are cool, make the frosting. Beat the butter until smooth and gradually add in the powdered sugar. Add the Bailey's and vanilla extract and beat to incorporate. Add additional Bailey's or milk if needed if the mixture is too stiff.
Frost and decorate the brownies and let sit for 30 minutes before cutting.