Preheat oven to 375° F. Grease a 9x13 baking dish with baking spray.
In a medium-sized bowl, add flour, cocoa powder, and salt. Whisk to combine and set aside.
In a medium-sized bowl, add semisweet chips, white chips and butter. Microwave in 20-30 second increments until just melted. Stir to combine well and set aside to cool slightly.
Using an electric mixer (or by hand), mix eggs, white sugar, brown sugar and vanilla until combined well. Slowly mix in melted chocolate.
Add the flour mixture and root beer alternately. Mix until just combined. Pour into prepared dish and bake for 35-40 minutes or until center is just set. Let cool completely before frosting.
To make frosting, beat butter and one cup of confectioners sugar at a time on medium speed until combined. Add root beer and root beer extract then continue mixing until frosting is smooth.
Add frosting to top of cooled brownies and spread evenly. Enjoy!