Preheat the oven to 350°. In a food processor, pulse the gingersnaps with 2 tablespoons of the sugar and a pinch of salt until fine crumbs form; add the softened butter and process until moistened. Using your fingers, press the gingersnap crumbs into the bottom of a buttered 9-inch springform pan in an even layer; brush any crumbs off the side of the pan. Bake the crust for about 10 minutes, until it is lightly browned. Let the crust cool slightly, then wrap the the bottom of the pan tightly in aluminum foil so it’s watertight. Set the pan in a large, deep skillet or a small roasting pan.
Rinse out the food processor bowl and wipe it dry. Add the softened cream cheese, pumpkin puree, vanilla extract and the remaining 2/3 cup of sugar to the food processor bowl and process for about 30 seconds, or until smooth. Add the eggs and pulse to blend. Add the flour, cinnamon, nutmeg and 1/2 teaspoon of salt and process for about 30 seconds, or until smooth. Carefully pour the pumpkin filling over the gingersnap crust. Set the skillet in the oven and carefully pour in enough hot water to reach halfway up the side of the springform pan. Bake the cheesecake for about 55 minutes, until the filling is barely jiggly in the center. Carefully transfer the skillet to a rack and let the cheesecake cool. Remove the aluminum foil and refrigerate the cheesecake until it is firm, at least 4 hours or overnight.
In a large skillet, cook the butter over moderately high heat until it is lightly browned and nutty-smelling, about 3 minutes. Add the pear wedges and cook, turning once, until they are softened and lightly browned, about 4 minutes. Add the sugar and cook, turning once, until the pears are lightly browned and glazed, about 1 minute longer.
Run a sharp knife around the edge of the cheesecake and remove the springform ring. Cut the pumpkin cheesecake into wedges and serve with the warm pears.