Preheat oven to 170 C / Gas 3. In a medium bowl, combine digestive biscuit crumbs and butter. Mix well and press into the bottom of a 23cm springform cake tin. Bake in preheated oven for 10 minutes.
In a microwave-safe bowl, microwave plain chocolate until melted. Stir occasionally until chocolate is smooth.
In a large bowl, beat the softened cream cheese, sugar and vanilla until creamy and smooth. Blend in the eggs one at a time. Remove about 250ml of the cream cheese mixture and combine with melted chocolate.
Spread plain mixture over the cooled biscuit base. Drop the chocolate mixture randomly over the top. With the tip of a knife, swirl the batter to create a marbled effect.
Bake in the preheated oven for 30 to 35 minutes, or until centre is set. Cool to room temperature, then refrigerate for 3 hours or overnight before serving.