Loosely roll a large piece of foil (about 20 inches long) into a 1-inch cylinder. Form a ring with the foil measuring about 7 inches in diameter. Fill a 6- to 7-quart slow cooker with 1/2 inch of water and place the foil ring in the bottom.
For the crust:
Add the gingersnaps to a food processor and process until crumbs form. Add 1/4 cup of the melted butter and a pinch of salt and pulse to combine. You want the mixture to look like wet sand. Brush an 8-inch springform pan with the remaining melted butter. Press the crumb mixture into the bottom and halfway up the sides of the pan.
For the filling:
Wipe out the food processor, add the cream cheese and brown sugar and pulse until smooth. Scrape down the sides, add the pumpkin puree, sour cream, vanilla extract and pumpkin pie spice and pulse until thoroughly combined. Add the eggs, pulsing until smooth and uniform. Pour into the crust.
Gently place the cheesecake on the foil ring in the slow cooker. Place a few layers of paper towels under the lid and cook on low heat for 4 hours. Allow the cake to cool in the slow cooker, about 2 hours.
Remove the cheesecake, cover with plastic wrap and refrigerate until well chilled, at least 3 hours and up to 3 days. Before serving, run a small knife around the edge of the cheesecake and remove the outer ring.
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