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Combine the cream cheese and sugar in a large mixing bowl and beat with an electric mixer on medium speed until light and fluffy—this will take several minutes; stop several times to scrape the sides and bottom of the bowl.
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Add the eggs and pumpkin and mix well to combine, then beat in the vanilla, cinnamon, and salt. Continue beating until mixture is smooth.
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Transfer about half of the filling to a smaller bowl and mix in the melted chocolate.
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Pour the plain pumpkin filling into the Oreo crust. Dollop the chocolate mixture over it.
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If desired, use the handle of a wooden spoon to swirl the chocolate and pumpkin together a couple of times. Don’t over-swirl and take care NOT to touch the crust with the spoon.
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Set the pan on a large baking sheet** and bake for 50 minutes to 65 minutes, until the center of the cheesecake barely jiggles when you tap the edge of the pan.
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Remove from the oven and immediately run a knife around the edge of the cheesecake. Cool completely on a wire rack, then cover with plastic wrap and refrigerate overnight.
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Slice and serve. Uneaten cheesecake can be stored in the refrigerator, covered, for up to 3 days or in the freezer, tightly wrapped, for up to 3 months.