Preheat the oven to 400 degrees F.  Lightly mist an 8-inch (straight-sided) cake pan with nonstick spray, and line with a circle cut from parchment.

Process the gingersnaps finely in a food processor.  Stir in the melted butter, and press the mixture into the bottom of the prepared pan.

In a large mixing bowl, mix the cream cheese, sugar, and flour on medium speed until well combined.

Add the eggs, one at a time, scraping the bottom and sides of the bowl with a silicone spatula after each addition.

Stir in the egg yolk, cream, vanilla, and salt, and pour the mixture over the gingersnap crust.

Place the cheesecake pan into a larger pan, and fill the larger pan with about an inch or two of hot water.  Bake for 20 minutes, then lower the oven temperature to 200 degrees F and bake for an additional 75-90 minutes, or until the cheesecake is set around the edges but still slightly jiggly towards the center.

Turn the oven off and prop the door open with a wooden spoon.  Allow the cheesecake to come to room temperature.  Chill completely in the refrigerator before inverting onto a serving platter.  Top with persimmon and whipped cream.

Core the persimmons and chop them roughly.  Place them in a small pot along with the sugar and water.  Cook over medium-low heat, stirring occasionally, until they are very soft.

Puree the mixture in a blender or food processor, until smooth.  Stir in the lemon juice.  Spread the mixture in an even layer over the cheesecake.

Whip the cream and powdered sugar until soft peaks form.  Pipe rosettes around the edge of the cheesecake.