In a medium saucepan, over low heat, stir together the chocolate, butter, and 2 tablespoons water until melted. Slightly beat the egg yolks and add to the chocolate, stirring constantly. Remove from heat and let cool.
While the chocolate custard is cooling, beat the egg whites until stiff; set aside. Gradually stir the sugar into the chocolate mixture. Beat until well combined. Stir in the vanilla and fold in the beaten egg whites. Line the sides of a 9- or 10-inch deep-dish pie plate or springform pan with the ladyfingers, trimming them to fit, if necessary. Spoon the chocolate mixture into the pie plate or pan and chill in the refrigerator for at least 4 and up to 24 hours.