In a medium-sized bowl, beat cream cheese and powdered sugar on medium speed until smooth and no lumps remain. Add Kahlua and mix well. In another bowl, or the bowl of a stand mixer with the whisk attachment, whip one cup of heavy whipping cream until still peaks form. Carefully fold the whipped cream into the cream cheese mixture.
In a shallow dish, stir together 2 ounces of Icebox Coffee concentrate and 1 cup milk.
Lining the springform pan with lady fingers works best if the lady fingers are the same height as the pan. Store bought lady fingers are taller than the height of the pan though, so you'll need to cut them to size. Hold one lady finger vertically in the pan and use a knife to trim it. Then use that lady finger as a guide to trim enough ladies to line the pan. (You don't HAVE to line the pan, though. If you'd like, you can skip this step and just assemble the layers.)
To create the bottom layer of the tiramisu, dip each lady finger in the coffee mixture for a couple seconds, turning the lady finger to coat. I suggest only dipping for a couple seconds because too long will create really soggy lady fingers. Place the lady fingers in the pan until the bottom is covered. (I cut some in half and in smaller pieces to cover it better.)
Next, cover the lady fingers with half of the cream cheese whipped cream. Top with a thin layer of chocolate shavings. Repeat the layers with more lady fingers, whipped cream, and chocolate shavings. Store the tiramisu in the fridge.
In the bowl of a stand mixer with the whisk attachment, whip the second cup of whipping cream until stiff peaks form. Pipe or spread whipped cream on top of the tiramisu and dust with cocoa powder. Store covered in the refrigerator until ready to serve.