In a medium saucepan, whisk together egg yolks and sugar until well blended. Whisk in milk and cook over medium heat, stirring constantly, until mixture boils. Boil gently for 1 minute, remove from heat and allow to cool slightly. Cover tightly and chill in refrigerator 1 hour.
In a medium bowl, beat cream with vanilla until stiff peaks form. Whisk mascarpone into yolk mixture until smooth.
In a small bowl, combine coffee and rum. Split ladyfingers in half lengthwise and drizzle with coffee mixture.
Arrange half of soaked ladyfingers in bottom of a 7x11 inch dish. Spread half of mascarpone mixture over ladyfingers, then half of whipped cream over that. Repeat layers and sprinkle with cocoa. Cover and refrigerate 4 to 6 hours, until set.