Step 1: Preheat your oven to 325°F (163°C). Prepare a 9-inch springform pan by lightly greasing it and lining the bottom with parchment paper. If using a water bath, wrap the outside of the pan securely with heavy-duty aluminum foil.
Step 2: For the crust, combine graham cracker crumbs, ¼ cup granulated sugar, and ½ teaspoon cinnamon in a medium bowl. Pour in the melted butter and mix until all crumbs are moistened. Press the mixture firmly into the bottom of the prepared springform pan.
Step 3: In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the softened cream cheese on medium speed until smooth, about 2 minutes.
Step 4: Add the light brown sugar and ¼ cup granulated sugar to the cream cheese. Beat until just combined, scraping down the sides of the bowl as needed.
Step 5: Mix in the sour cream until smooth. Add the eggs one at a time, beating on low speed until just incorporated after each addition. Do not overmix.
Step 6: Stir in the canned pumpkin puree, vanilla extract, and pumpkin pie spice until the mixture is uniform and smooth.
Step 7: Pour the cheesecake filling over the graham cracker crust in the springform pan. Smooth the top with a spatula.
Step 8: Place the springform pan inside a larger roasting pan. Carefully pour hot water into the roasting pan, ensuring the water level comes about halfway up the sides of the springform pan.
Step 9: Bake for 1 hour and 20 minutes, or until the edges are set but the center still has a slight jiggle when gently shaken.
Step 10: Turn off the oven, but leave the cheesecake inside with the oven door propped open slightly for 1-2 hours to cool gradually.
Step 11: Remove the cheesecake from the water bath and cool completely on a wire rack for at least 30 minutes. Then, transfer to the refrigerator and chill for a minimum of 4-6 hours, or preferably overnight, before releasing from the pan.
Step 12: Just before serving, drizzle generously with caramel sauce. Slice and enjoy!