Pure Pumpkin Cheesecake

Prepare the oven and pan

1. Spray a 9-inch (23-cm) springform pan that has sides 2 1/2 to 3 inches (7 to 8 cm) deep with nonstick cooking spray. Wrap the outside of the pan with a double layer of heavy-duty aluminum foil to prevent leakage. Also make sure you have a 12-by-2-inch (30-by-5-cm) round cake pan or a large roasting pan.

Make the gingersnap crust

1. Preheat the oven to 350°F (175°C) and adjust the oven rack to the lower third of the oven.
2. Spread the pecans evenly on a rimmed baking sheet and bake for about 7 minutes, stirring once or twice to ensure even toasting. Immediately transfer the toasted nuts to a plate and let cool before using.
3. In a food processor, combine the gingersnap crumbs, pecans, sugar, and salt and process until fine crumbs form, about 20 seconds. Add the melted butter and pulse just until incorporated, about 10 times.
4. Using your fingers or the back of a spoon, press the crumb mixture into the bottom of the pan and partway up the sides. Using a flat-bottomed, straight-sided measuring cup or a 6-inch (15-cm) round cake pan, smooth the crumbs evenly over the bottom of the pan and at least 1 1/2 inches (4 cm) up the sides.☞ TESTER TIP: To keep the crumbs from sticking to your fingers, place a piece of plastic wrap over the crumbs and press them into the pan through the wrap.

Make the pumpkin filling

1. In a small, heavy saucepan over medium heat, stir together the pumpkin and sugar and, stirring constantly, bring the mixture to a sputtering simmer. Reduce the heat to low and cook, stirring constantly, until thick and shiny, 3 to 5 minutes.
2. Using a silicone spatula, scrape the mixture into a large food processor and process for 1 minute with the feed tube open. With the motor running, add the cold cream. Then add the cream cheese in several pieces and process for 30 seconds, or until smoothly incorporated, scraping down the sides of the bowl 2 or 3 times. Add the eggs and yolks and process just until incorporated, about 5 seconds.
3. Using the silicone spatula, scrape the filling into the prepared pan. Smooth the surface evenly with a small offset spatula. Place the pan in the larger cake or roasting pan and add enough very hot water to the larger pan to reach a depth of 1 inch (25 mm).
4. Bake the pumpkin cheesecake, turning the pan halfway after the first 25 minutes, for 45 minutes. Turn off the oven—without opening the door or peeking in any way—and let the cheesecake cool for 1 hour.
5. Place the pan on a wire rack and let cool to room temperature, about 1 hour. Cover the cheesecake with a large overturned bowl or plastic wrap and refrigerate overnight. 

Make the caramel glaze

1. Have ready a 1-cup heatproof glass measure coated lightly with nonstick cooking spray.
2. In a medium heavy saucepan, preferably nonstick, stir together the sugar, corn syrup, and water until all the sugar is moistened. Heat, stirring constantly, until the sugar dissolves and the syrup is bubbling. Stop stirring completely and allow the mixture to boil, undisturbed, until the mixture turns a deep amber [360°F (180°C) or a few degrees lower because its temperature will continue to rise].
3. Remove the pan from the heat as soon as it reaches temperature. Immediately but slowly and carefully pour the hot cream into the caramel. It will bubble up furiously. Use a silicone spatula or wooden spoon to stir the mixture gently, scraping the thicker part that settles on the bottom.
4. Return the pan to very low heat, continuing to stir gently, for 1 minute, until the mixture is uniform in color and the caramel is fully dissolved. Remove it from the heat and gently stir in the butter until incorporated. The mixture will be a little streaky but becomes uniform in color once cooled and stirred.
5. Pour the caramel into the prepared glass measure and let it cool for 3 minutes. Gently stir in the vanilla and allow the caramel to cool until no longer warm to the touch, stirring gently 3 or 4 times. (The glaze keeps, covered, for up to 3 days at room temperature and for 3 months refrigerated. To reheat, place the caramel in a heatproof glass container, if it isn't already in one, and place the container in a pan of simmering water until warm, about 7 minutes, or microwave it on high for 1 minute, stirring twice.)

Assemble the cheesecake

1. To unmold the cheesecake, wipe the sides of the pan with a dish towel that you've run under hot water and wrung out. Then carefully remove the side of the pan.
2. Pour the caramel glaze over the pumpkin cheesecake from the glass measure or, for greater precision, use a pastry bag fitted with a small decorating tip,or a resealable plastic bag with a very small semicircle cut from one corner. Slice and serve and be ready to listen to oohs and aahs.