Step 1: Prepare the Coffee Mixture. Brew strong coffee and let it cool completely. Stir in the Kahlua or coffee liqueur if using. Set aside.
Step 2: Create the Egg Yolk Mixture. In a heatproof bowl set over a saucepan of simmering water (bain-marie), whisk together the egg yolks and granulated sugar. Whisk constantly for 5-7 minutes, until the mixture is pale yellow, thick, and registers 160°F (71°C) on an instant-read thermometer. Remove from heat and let cool slightly.
Step 3: Make the Mascarpone Cream. In a large bowl, beat the softened cream cheese until smooth. Add the softened mascarpone cheese and vanilla extract, beating until just combined and smooth. Gently fold the cooled egg yolk mixture into the mascarpone mixture until no streaks remain.
Step 4: Whip the Heavy Cream. In a separate cold bowl, whip the heavy cream until stiff peaks form. Gently fold the whipped cream into the mascarpone mixture in two additions until fully incorporated and light. Be careful not to overmix.
Step 5: Assemble the First Layer. Quickly dip each Oreo cookie into the cooled coffee mixture for just 1-2 seconds per side (don’t let them get too soggy). Arrange a single layer of soaked Oreos at the bottom of a 9×13 inch baking dish. You may need to break some cookies to fit gaps.
Step 6: Layer the Cream and Oreos. Spread half of the mascarpone cream mixture evenly over the first layer of Oreos. Repeat with another layer of coffee-soaked Oreos, then top with the remaining mascarpone cream, spreading it smoothly to the edges.
Step 7: Chill and Dust. Cover the dish tightly with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow the flavors to meld and the dessert to set properly. Before serving, dust generously with unsweetened cocoa powder and garnish with chocolate shavings or extra crushed Oreos.