Preheat oven to 350°F. Wrap outside of a 9-by-3-inch springform pan with heavy-duty foil. Grease inside of pan with butter, then set aside.
Make crust: Combine graham cracker crumbs, 3 Tbsp. sugar and cocoa powder, stirring with a fork. Add butter and stir until incorporated. Press mixture into bottom of pan. Bake for 10 minutes; let cool on wire rack.
Make filling: Place chocolate in a small bowl and microwave at medium for 2 1/2 minutes; stir. Microwave at medium for 30 more seconds and stir; repeat, if necessary, until melted and smooth. Reserve.
Beat cream cheese and 1 cup sugar at high speed until fluffy, about 5 minutes. Add eggs all at once and mix at medium speed until thoroughly blended. Add cream and vanilla extract; mix until blended.
Transfer 1 cup batter to bowl with melted chocolate; stir to mix. Scrape half of plain batter into cake pan on top of crust. Dollop chocolate batter on surface. Scrape remaining plain batter on top of chocolate. Swirl batters together with a rubber spatula for a marbleized effect.
Place cake pan in a roasting pan, add 1 inch of hot tap water to roasting pan and bake for about 1 hour and 10 minutes without opening oven door. (Cake should only barely jiggle when pressed in center.) Transfer cake from water to rack and cool for 1 hour. Chill until cold.
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