Heat 1/2 cup butter, milk, and marshmallows in a saucepan over medium heat, stirring often, until marshmallows are melted, about 5 minutes. Remove from heat; whisk in 1/4 cup cocoa. Gradually stir confectioners' sugar into marshmallow mixture until smooth. Spread frosting over peanut butter layer of brownies. Chill in refrigerator until set, about 20 minutes.