Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper or foil, leaving an overhang on all sides. Spray with nonstick cooking spray.

In a food processor, pulse the crackers until finely ground. Add the butter and pulse until moistened. Press the crumb mixture into the bottom of the prepared pan using the bottom of a measuring cup or glass. Bake until fragrant, about 10 minutes. Place on a cooling rack to cool completely. Maintain oven temperature.

In a large bowl, use an electric mixer to beat the cream cheese, sugar, and pumpkin at medium-high speed until smooth. Add the eggs, one at a time, and beat until combined. Add the flour, spices, and salt and beat until combined. Be careful not to overbeat.

Place the chopped chocolate in a microwave-safe bowl; microwave in 30-second bursts, stirring between each, until melted and smooth. Add 1 cup cheesecake batter and stir to combine.

Pour the pumpkin cheesecake batter into the prepared pan.

Drop dollops of the chocolate batter mixture and swirl with a butter knife. Bake at 350°F until the edges are slightly golden and the cheesecake is set but still slightly jiggly in the center, about 40 minutes. Do not overbake.

Place the cheesecake on a cooling rack to cool completely in pan. Cover and chill in the fridge until firm, at least 4 hours and up to 2 days. Using the overhang, transfer cheesecake to a cutting board to cut into squares before serving.