In a medium saucepan, whisk together egg yolks and sugar until well blended. Stir in milk. Bring to a boil over medium heat, whisking constantly.
Boil for 1 minute; remove from heat. Pour into a bowl and cover with plastic wrap, placing wrap directly on the surface of the custard. Refrigerate until chilled, at least 1 hour. Remove mascarpone cheese from the refrigerator so it softens while the custard chills.
In an electric mixer fit with the paddle attachment, or in a large bowl with a spatula, blend chilled custard with softened mascarpone cheese until smooth. Set aside.
To make the whipped cream, in an electric mixer fit with the whisk attachment, or with an electric hand mixer, beat cream and vanilla until stiff peaks form.
In a small bowl, combine chilled espresso and rum. Separate the lady fingers horizontally and arrange a single layer in the bottom of an ungreased 11-inch by 7-inch baking dish (about 16 lady fingers).
Brush with the espresso-rum mixture. Spread half of the custard mixture over the lady fingers, then top with half of the whipped cream.
Repeat with remaining lady fingers brush with the espresso-rum mixture, remaining custard mixture, and remaining whipped cream. Sprinkle with cocoa as desired (1 tablespoon or up to ¼ cup). Refrigerate at least 4 hours or up to 24 hours. Store covered in the refrigerator.
