Preheat oven to 300 degrees (F).
Microwave chocolate on High 45 to 60 seconds, stirring once halfway through microwaving, until melted. Set aside.
Mix together cream cheese and sugar until smooth and creamy.
Add eggs, one at a time, beating until smooth. Stir in liqueur.
Pour filling evenly over crusts.
Drop melted chocolate randomly onto filling. Let it sink, then with a knife, cut through chocolate and filling to swirl to marble.
Bake 1 hour, 10 minutes until set. Turn oven off and open door slightly. Cool cheesecake in oven 1 hour.
Remove from oven and cool at room temperature for 1 hour. Refrigerate 3 hours.
Garnish with whipped cream and shaved chocolate if desired, right before serving.