Preheat the oven to 325 degrees F. Wrap the outside (bottom and side) of a 9-inch springform pan with foil. Make the crust: Pulse the cookies and sugar in a food processor until finely ground. Add the melted butter; pulse to combine. Press into the bottom and about 1/4 inch up the side of the pan. Brush the side of the pan lightly with melted butter. Bake until golden and set, 12 to 15 minutes. Transfer to a rack; cool completely.
Make the filling: Drain the ricotta in a fine-mesh sieve, 20 minutes. Combine with the sugar in the food processor; pulse until smooth. Add the pumpkin, eggs, mascarpone, vanilla, pie spice and salt; pulse until combined. (Do not overmix.) Pour the filling into the cooled crust. Bake until set around the edge but the center still jiggles slightly, 1 1/2 hours to 1 hour 45 minutes. Transfer to a rack and let cool to room temperature. Cover and refrigerate until cold and set, at least 8 hours or overnight.
Make the topping: Chop 1 cup cranberries and put in a small saucepan with the sugar, lemon juice, salt and 1/3 cup water. Cook over medium heat until thick, 7 to 10 minutes. Stir in the remaining 3/4 cup whole cranberries; cook 2 more minutes. Let cool.
Let the cheesecake sit at room temperature 20 minutes, then run a thin knife around the edge and remove the springform ring. Add a splash of water to the cranberry topping to loosen, if needed, then spread over the cheesecake.
Photograph by Kana Okada
Recipe courtesy of Food Network Magazine