Whisk together first 4 ingredients in a small saucepan. Cook over medium heat, whisking constantly, 5 minutes or until thickened. Spoon mixture into a small bowl; cover surface of mixture with plastic wrap, pressing wrap onto surface, and let stand 30 minutes or until cool.
Beat butter and sugar at medium speed with an electric mixer until light and fluffy. Gradually add cooled cocoa mixture, 1 tablespoon at a time, beating until blended after each addition. Add vanilla, beating until mixture is the consistency of whipped cream.