Preheat the oven to 350°F. Grease an 8-inch springform pan and set aside.
Place the gluten free Oreos, sugar, butter, and salt into a food processor, and puree until finely ground. Press crumb mixture firmly into the bottom of the springform pan. Place in the oven and bake for 5-8 minutes, or until the mixture is lightly browned and set. Remove from the oven and set aside while you prepare the cheesecake batter.
Reduce the oven temperature to 300°F. Wrap the bottom of the pan with aluminum foil.
In the bowl of a stand mixer, combine the cream cheese and sour cream. Beat on medium speed until smooth. Scrape down the sides of the bowl, and repeat. Add the sugar and, and beat the mixture on medium speed until combined. Scrape down the sides of the bowl. Turn the mixer on high, and cream together until light and fluffy, about 4 minutes.
Once the mixture is light and fluffy, add eggs one at a time, scraping down the sides and bottom of the bowl in between additions. Add the vanilla extract and salt. Turn the mixer on low speed until just combined. Remove the bowl from the mixer, and gently fold in the gluten free Oreos, ensuring that all ingredients are very well incorporated.
Pour batter into the prepared pan and place onto a sheet pan with at least a 1-inch lip. Place the sheet pan in the oven, and gently pour warm water into the pan, until it is about ½ inch deep. Bake for 40-45 minutes, or until the center is set, but still jiggles slightly. Check the cake halfway through baking, and if needed, loosely lay a piece of foil over the cake to prevent it from overbrowning.
Once the cake is baked, turn the oven off, and let the cake remain in the oven until the oven is completely cool, about 1-2 hours. Remove the cake from the water bath, and gently cover. Place in the refrigerator until the cake is completely chilled, 4-6 hours or overnight. Remove the springform from the pan, and cut into 12 slices before serving.