In a small bowl, mix Kahlua and espresso powder together and set aside to dissolve.
In a large bowl, beat together cream cheese, coconut milk, sugar, and salt until smooth and creamy. Add the Kahlua espresso mixture and beat to combine.
Pour mixture into a frozen ice cream canister and process according to manufacture's instructions, about 20 minutes.
When there is one minute left, pour an 1/8th of a cup or so of Kahlua into a small bowl. Quickly dip each lady finger into the Kahlua and set aside.
Scrape ice cream out of canister and place in a large plastic container.
Stir in the lady fingers, making sure they don't clump together. You want them evenly distributed. Cover with a lid, and place in the freezer.
One to four hours in the freezer will give you a "soft-serve" type of ice cream. Overnight, and your ice cream will be firm, but not rock hard. Alcohol does not freeze, so your ice cream will remain softer than regular ice cream.
Scoop ice cream into bowls and dust with cocoa powder {if desired} and serve.
Notes
To make regular Tiramisu Ice Cream: substitute mascarpone or regular cream cheese and half and half for the coconut milk.