Cut the ladyfingers in 4 using your hands or a knife. Soak them in the coffee very little: they should go in and out of the coffee. Soak only a couple of pieces each time, let them drip the excess coffee, and place them in the bowl with the ice cream mix. Once they are all in, fold them into the ice cream. Don't over mix or they will disintegrate.
Pour about 1/3 of the mix into a container or pan that's freezer safe. Use a small sieve or colander to make a thin layer of cocoa powder on top. Repeat with the remaining 2 layers. Before the last layer of cocoa powder you can use the back of a spoon to give the ice cream texture so that it looks pretty.
Freeze the ice cream for 8 hours or overnight. Remove it from the freezer a few minutes before serving.