In a medium saucepan, whisk together 6 egg yolks and ¾ cup sugar until well blended. Whisk in ⅔ cup 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 place in refrigerator for 20 minutes to cool.
In a medium bowl, beat 1 ¼ cups cream with ½ teaspoon vanilla until stiff peaks form.
Whisk 1 ¼ cup mascarpone into yolk mixture until smooth.
In a small bowl, combine ½ cup coffee and 4 Tablespoons rum. Place ladyfingers on a plate and drizzle coffee mixture over until ladyfingers soak up all the coffee.
Arrange half of soaked ladyfingers in bottom of a 8x8-inch or comparable size pan (breaking some in half if necessary to cover entire bottom). Spread half of mascarpone mixture over ladyfingers, then half of whipped cream over that. Repeat layers one more time.
Cover and refrigerate 24 to 48 hours.
Just before cutting to serve, sprinkle top with 1 Tablespoon cocoa powder.