For the crust: In a large bowl, combine the graham cracker crumbs, butter and sugar. Press into a 9-inch springform pan, pushing the crumbs up the sides. Put the pan in the freezer to chill.
For the filling: Microwave the chocolate and butter in a microwave-safe bowl until melted, about 1 minute. Set aside.
Beat together the cream cheese, sugar and vanilla in a large bowl with an electric mixer on medium speed until light and fluffy. Beat in the eggs 1 at a time until well combined. Mix in the cream. Transfer 2 to 3 cups of the batter to a smaller bowl and stir in the melted chocolate mixture. Pour the remaining batter into the chilled crust. Drizzle in the chocolate batter and swirl with a knife.
Bake for 15 minutes, then reduce the oven temperature to 300 degrees F and bake until the outside is set and the very center just wobbles slightly, about another hour. Turn off the oven and let the cheesecake cool in the oven for 30 minutes. Serve at room temperature or chilled.