Preheat oven to 325ºF (160ºC).
Stir crumbs with butter and instant coffee granules until well moistened. Press onto bottom of greased 9-inch (2.5 cm) springform pan. Centre pan on large square of foil; press foil to side of pan. Bake in centre of oven until set, about 10 minutes. Let cool.
Meanwhile, in bowl over saucepan of hot (not boiling) water, melt chocolate, stirring; let cool to room temperature.
In large bowl, beat cream cheese until smooth. Beat in sugar, scraping down sides often. Beat in eggs, one at a time, beating well after each addition and scraping down bowl often. Beat in cream, coffee liqueur and cooled chocolate until smooth.
Remove two-thirds of the batter into large bowl. Whisk melted bittersweet chocolate into remaining batter. Pour darker chocolate batter into prepared crust. Using offset spatulas, smooth top. Pour lighter batter over top, smooth top.
Set cheesecake in larger pan; pour in enough hot water to come 1-inch (2.5 cm) up sides. Bake in centre of oven for about 1 hour or until set around edge and centre is still jiggly. Turn off oven; let stand in oven for 1 hour.
Transfer springform pan to rack and remove; let cool completely. Cover with plastic wrap and refrigerate for at least 4 hours or until chilled. (Make-ahead: Refrigerate for up to 3 days or freeze in airtight container for up to 2 weeks.)