Beat egg yolks and sugar in a medium saucepan. Whisk until well blended. Whisk in milk. Over medium heat, bring mixture to boil, stirring constantly. Reduce the heat to low. Boil and stir for 1 minute. Remove from heat.
Place plastic wrap or waxed paper directly onto the egg yolk mixture in the saucepan. Refrigerate for 1 hour.
Mix egg yolk mixture and cheese with whisk until smooth. Beat whipping cream and vanilla in chilled medium bowl with electric mixer on his speed until stiff.
Separate ladyfingers horizontally, in half, Mix espresso and rum (or rum extracts + 2 tbsp water). Drizzle ladyfingers with espresso mixture.
Arrange half of the ladyfingers in a single layer in 9x13 baking dish. Spread half of the cheese mixture then half of the whipped cream over the ladyfingers. Repeat layers.
Sprinkle top generously with cocoa. Cover and refrigerate 4-6 hours or overnight.