Preheat oven to 325°F (165°C) with a rack in the center position.
Pulse graham crackers in a food processor until they form fine, even crumbs. Add brown sugar and salt, pulse to combine. Pour in melted butter and pulse until mixture looks like wet sand and holds together when pressed.
Press the crumbs firmly into the bottom of a 9 inch springform pan using the bottom of a measuring cup to pack it evenly. Bake for 10 minutes, then set aside to cool.
Pour the apple cider into a medium saucepan and bring to a gentle boil over medium heat. Reduce heat and let simmer, stirring occasionally, for 20-25 minutes until reduced to about 1/2 cup and slightly syrupy. Let cool completely before adding to the batter.
In a large bowl, beat the softened cream cheese on medium speed until completely smooth with no lumps. Add sugar and flour, beat again until incorporated. Mix in sour cream, vanilla, cinnamon, and salt until smooth and creamy.
Pour in the cooled, reduced apple cider and beat on low speed until evenly blended. Add eggs one at a time, mixing on low speed and stopping as soon as each one is combined to avoid overbeating.
Wrap the outside of the springform pan tightly in two layers of heavy duty foil, covering bottom and sides completely. Pour the filling over the cooled crust and smooth the top with a spatula.
Set the wrapped pan inside a large roasting pan, then carefully pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan. Bake at 325°F for 1 hour to 1 hour 20 minutes, until edges are set and center still jiggles slightly.
Turn off the oven, crack the door open a few inches, and let the cheesecake sit inside for 1 hour. Remove from water bath and foil once cool enough to handle. Let cool to room temperature on the counter.
Cover and refrigerate for at least 6 hours, or overnight for the cleanest slices.
Stir together sugar and cinnamon for the topping. Brush melted butter evenly over the top of the chilled cheesecake. Sprinkle the cinnamon sugar mixture over the buttered surface. Run a thin knife around the edge of the pan before releasing the springform sides, then slice and serve.