Whisk egg yolks and sugar over double boiler over low heat until thick.
Add mascarpone and 1 tbsp dark rum to bowl and whip with hand mixer until thick.
Combine whipped mascarpone with egg and sugar mixture. Set aside.
Using spoon, mix 2 tbsp dark rum with espresso coffee in a bowl. Set aside.
To assemble, dip ladyfingers into coffee and rum mixture and place onto baking dish. Use spatula to spread half of the mascarpone mixture over the ladyfingers. Repeat for the next layer. Sift cocoa powder over tiramisu.
Place tiramisu in refrigerator for at least 4 hours.