Fill a roasting pan halfway with water and set on a rack in the lower third of the oven; position another rack in the middle and preheat to 325 degrees F. Wrap the outside (bottom and side) of a 9-inch springform pan with foil. Make the crust: Pulse the gingersnaps in a food processor until finely ground. Add the melted butter and brown sugar and pulse to combine. Press into the bottom and about 1 inch up the side of the prepared pan; set aside.
Prepare the pears: Melt the butter in a large skillet over medium-high heat. Add the pears, sprinkle with the granulated sugar and cook, stirring occasionally, until the pears are tender and lightly browned around the edges, 5 to 7 minutes. Add the molasses and continue cooking until syrupy, about 2 more minutes; set aside.
Make the filling: Beat the Neufchatel cheese and granulated sugar in a large bowl with a mixer on medium speed until smooth and creamy, about 2 minutes. Add the eggs, one at a time, beating well after each addition. Add the vanilla and flour and beat until just combined, then add the sour cream and beat until smooth, about 1 more minute.
Pour the filling into the prepared crust. Gently arrange the pear slices on top; set aside any extra molasses syrup at room temperature for serving. Transfer the cheesecake to the oven, placing it on the middle rack directly over the water bath. Bake until lightly browned and set around the edge but the center still jiggles slightly, about 1 hour 15 minutes. Transfer to a rack and let cool to room temperature, then cover and refrigerate until cold and set, at least 6 hours or overnight. Let the cheesecake sit at room temperature 20 minutes, then run a thin knife around the edge and remove the springform ring. Drizzle with the remaining molasses syrup.