Beat yolks in bowl until thick and lemon-colored. Gradually beat in 1 cup sugar until very light in color, 5 to 7 minutes. Beat in milk. Mix yolk-milk mixture, remaining 1 cup sugar and butter in saucepan. Bring to boiling over medium heat, whisking occasionally, 12 to 15 minutes. Boil, whisking, 1 minute. Remove from heat. Stir in chocolate until melted, and add vanilla. Transfer to bowl. Refrigerate 30 minutes, until spreading consistency.