Whisk together the eggs and sugar in a large bowl. Or a double boiler if you have one, I don’t, so I just use a metal bowl.
Put the boil over a pot of simmering water.
Whisk constantly until the eggs triple in volume and turn pale yellow. It takes about 5 minutes.
Now that I am reading this recipe again, it would have been smart of me to use the bowl of the mixer, instead of transferring it to the mixer bowl. Oops. Pour the eggs into the mixer and beat for about 5 minutes. The bowl will feel cool when it is ready.
Add the mascarpone, one tub at a time until it is combined.
Fold in the chocolate chips. Chill for at least one hour.
In a large bowl, stir together the boiling water, brown sugar, espresso powder, and Kahlua. Stir until everything has dissolved. Set aside and let cool.
Pour the coffee mixture into a shallow dish. Dip the ladyfingers into the mixture, and line the bottom of a 9×13 pan with the cookies.
Layer 1/3 of the mascarpone mixture over the ladyfingers. Repeat the layers until you have 3 layers of each. Alternate the direction of the cookies, it helps the tiramisu hold together when you cut it. Cover and chill for 2 hours. Overnight is even better. The longer is chills, the better it is.
Cover the top with shaved chocolate before serving.