In a large bowl, beat the other softened stick of butter for approximately 30 seconds with mixer on medium speed. Add the cooled brown butter and beat together well. Add the vanilla and the sugar and continue to beat. Adding 1T of buttermilk at a time, beat in until the frosting is the desired spreading consistency. If frosting is still too stiff with 3T. of buttermilk, up to 3 more can be added. Too much, just add a little additional sugar until desired consistency is achieved.