For the crust: Preheat the oven to 350 degrees F. Place a 9-by-13-inch baking pan of hot water on the bottom oven rack.
Line a second 9-by-13-inch baking pan with foil, leaving an overhang around the edges, and coat with cooking spray. Pulse the graham crackers in a food processor until fine crumbs form. Pour in the butter and pulse until the crumbs are well coated and stick together when pinched. Press evenly into the bottom of the foil-lined pan.
For the filling: Add the cream cheese, granulated sugar, sour cream, lime juice, vanilla and eggs to the food processor (no need to clean it first). Process until smooth, using a spatula to scrape the sides as needed.
Pour the filling over the crust and smooth the surface. Bake on the center rack until the center is just set but slightly jiggly, about 45 minutes. Turn off the oven and leave the pan in the oven with the door closed for 10 minutes. Open the door halfway and leave the pan in the oven until the cheesecake is firmly set around the edges and very slightly jiggly in the center, about 10 more minutes. Remove from the oven and let cool to room temperature, about 30 minutes, then refrigerate until cold, at least 1 hour and up to 24 hours.
When ready to serve, lift the cheesecake out of the pan using the foil overhang. Cut into 12 large pieces (or 24 small pieces if preferred) and place on a serving platter. Generously dust with powdered sugar and grate over lime zest.
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