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 flat bowl, combine coffee and rum. Split sponge fingers or savoiardi in half lengthwise and drizzle with coffee mixture.
Arrange half of soaked biscuits in bottom of a 18x28cm dish. Spread half the mascarpone mixture over biscuits, then half of whipped cream over that. Repeat layers and sprinkle with cocoa. Cover and refrigerate 4 to 6 hours, until set.