Position a rack in the center of an oven and preheat to 325ºF. Butter a 9-inch springform pan and cover the outside with aluminum foil, shiny side out.
In a mixing bowl, combine the graham cracker crumbs and granulated sugar and stir to mix. Add the butter and stir until blended. Press the mixture evenly into the bottom and halfway up the sides of the pan. Refrigerate until ready to use.
In a small saucepan over low heat, combine the chocolate and rum and melt, stirring often, about 1 minute; set aside.
In the bowl of an electric mixer, beat the cream cheese until smooth and fluffy. Gradually add the superfine sugar and continue beating until blended. Then beat in the sour cream and vanilla extract. Add the eggs one at a time, beating well after each addition.
Remove the bowl from the mixer and set it over a pan of simmering water but not touching the water. Warm the mixture, stirring constantly, until completely smooth and very creamy, 2 to 3 minutes.
Pour 1 1/3 cups of the batter into another bowl and set aside. Add the chocolate mixture to the remaining batter and whisk until blended. Set the bowl back over the simmering water and stir until creamy and smooth.
Pour the chocolate batter into the prepared pan. Gently pour the plain batter over the top and make swirls in the batter with a fork.
Bake until the cake is set around the edges and the center is still a little loose, 45 to 50 minutes. Cool to room temperature, remove the rim from the pan and refrigerate overnight.