Preheat oven and prepare baking pan: Preheat your oven to 350 F degrees. Line a 9x9 inch baking pan with parchment paper. Set aside.
Combine dry ingredients: In a bowl add the flour and sift the cocoa powder, add the salt then whisk everything together. Set aside.
Combine wet ingredients: In the bowl of your mixer add the butter, brown sugar, granulated sugar, vanilla extract and eggs.
Combine wet and dry: Mix everything together until well incorporated, about 1 minute. Add the beer and mix for another minute. Finally add cocoa and flour mixture and mix until batter is smooth.
Transfer batter to baking pan: Pour half the batter in the prepared baking dish, then top with the chocolate chips evenly, then top with the remaining batter.
Bake: Bake for 45 minutes. To test if it's done, insert a toothpick in the center of the brownies and if it comes out clean, it's done. Let cool completely.
Make frosting: Meanwhile, make the buttercream frosting. Add beer to a saucepan and cook on low heat for about 10 minutes until it reduces and thickens, it will be similar to a syrup. You should have about 1/4 cup left.
In a stand mixer, cream butter, then add the icing sugar and vanilla extract. Add about 2 tbsp of the Guinness extract and mix well. You might not need all the Guinness extract. Gradually add milk to the frosting and beat until smooth. If frosting is too thick add in a bit more milk or the Guinness extract, a few drops at a time.
Frost brownies: When the brownies have cooled, remove from pan and spread the buttercream frosting over the top. Sprinkle with chocolate shavings, then cut into pieces.