Preheat oven to 325°F (163°C). Grease a 9-inch springform pan. Mix cookie crumbs with melted butter and press into the pan base. Set aside.
In a large bowl, beat cream cheese and sugar until smooth. Add eggs one at a time. Stir in vanilla extract and sour cream.
Split the batter into two bowls. Mix espresso into one half until fully combined.
Pour plain batter into the crust. Gently layer the coffee cheesecake batter on top. Use a skewer or knife to create a marble swirl effect.
Drizzle ganache over the top and lightly swirl.
Bake for 55–65 minutes, or until the center is nearly set. Turn off oven, crack door, and cool inside for 1 hour.
Refrigerate for at least 4 hours, ideally overnight.
Top with whipped cream, cocoa powder, or shaved chocolate before serving.