Preheat oven to 350°F (175°C). Grease a 9-inch springform pan and set aside.
In a medium bowl, combine gluten-free graham cracker crumbs, melted butter, 1/4 cup sugar, and 1/2 teaspoon cinnamon. Press firmly into the bottom and 1 inch up the sides of the prepared pan.
Bake the crust for 10 minutes. Remove from oven and let cool completely on a wire rack. Reduce oven temperature to 325°F (160°C).
Wrap the outside of the cooled springform pan in three layers of heavy-duty aluminum foil to prevent water from entering during the water bath.
In a stand mixer fitted with the paddle attachment, beat the cream cheese and sour cream on medium speed until smooth and free of lumps. Scrape down the sides of the bowl.
Add the granulated sugar and brown sugar. Beat on medium-high for 2 minutes until light and fluffy.
Incorporate the pumpkin puree, vanilla extract, pumpkin pie spice, and salt. Mix on medium speed until fully combined.
Reduce mixer speed to low. Add eggs one at a time, mixing just until the yellow disappears after each addition. Do not overmix to avoid incorporating excess air.
Pour the batter over the crust. Place the springform pan into a large roasting pan. Pour boiling water into the roasting pan until it reaches halfway up the sides of the springform pan.
Bake for 75 to 85 minutes, or until the edges are set and slightly puffed, but the center still has a slight wobble.
Turn off the oven and crack the door open about 1 inch. Allow the cheesecake to cool slowly inside the oven for 1 hour.
Remove the pan from the water bath and take off the foil. Run a thin knife around the edge of the cake. Let cool to room temperature on the counter.
Refrigerate the cheesecake for at least 6 hours, preferably overnight, before slicing and serving.