Preheat oven to 325 degrees F (165 degrees C).
Chop the walnuts in a food processor until fine. Mix together in a bowl with the brown sugar and melted butter. Press the mixture into the bottom of a 9-inch springform pan.
Bake in the preheated oven for 12 minutes. Set aside to cool completely.
Combine the persimmons, cream cheese, 1 1/4 cup sugar, 3/4 cup sour cream, cinnamon, and ginger in a food processor. Blend in processor until smooth, stopping occasionally to scrape edges of food processor bowl with a spatula. Add the eggs, one at a time, and process until fully incorporated. Pour the mixture over the cooled crust.
Bake in the preheated oven until mostly set with the center being slightly jiggly, 60 to 75 minutes.
While the cheesecake is baking, whisk together the 1 1/4 sour cream, 3 tablespoon white sugar, and vanilla extract. Spread evenly over the cheesecake while still hot and return to oven another 10 minutes. Allow to cool completely. Loosely cover with aluminum foil and refrigerate 4 to 8 hours or overnight before serving.
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