Preheat oven to 350 degrees. Line bottom and sides of an 8-inch square baking pan with parchment paper or aluminum foil, leaving an overhang on all sides. Set aside.
In a food processor, blend cookies until finely ground (you should have about 1 cup crumbs); add butter, and pulse until moistened.
Transfer crumb mixture to prepared pan, and press gently into bottom. Bake about 10 minutes. Set aside to cool.
Place cream cheese in food processor; blend until smooth. Add sugar, pumpkin puree, eggs, flour, pumpkin-pie spice, and salt; process until combined. Set aside.
Place chocolate in a microwave-safe bowl; microwave in 30-second increments, stirring between each, until melted. Add 1 cup pumpkin mixture; stir to combine. Set aside.
Pour remaining pumpkin mixture into prepared pan. Drop dollops of chocolate mixture onto pumpkin mixture; swirl with a knife. Bake until cheesecake is set but jiggles slightly when gently shaken, 40 to 50 minutes.
Cool in pan. Cover; chill until firm, at least 2 hours (and up to 2 days). Transfer cake to work surface. With a knife dipped in water, cut into 16 squares. Serve.
Gluten Free: You can use gluten free chocolate cookies, and rice flour in the filling to make this gluten free.