Preheat the oven to 350?, and grease a 9-inch circle springform pan with non-stick baking spray. Cover the bottom of the pan with aluminum foil to prevent any batter from dripping out of the pan.
To make the crust, pulse the graham crackers in a food processor. Then, add in the pecans, butter and brown sugar and pulse again on high speed. Blend until smooth and crumby.
Press the crust mixture onto the bottom and 2 inches up the sides of the pan.
Bake for 12 minutes.
Cool completely on a wire cooling rack.
To make the cheesecake filling, mix together the cream cheese, sugar, flour, pumpkin pie spice, and salt in a food processor or large blender. Add sour cream and vanilla. Blend until combined.
Add in 1 egg at a time into the cheesecake batter and blend in between each addition.
Remove ¾ cup of batter and set aside.
In a small bowl or measuring cup, stir together ¼ cup of hot/boiling water with the instant coffee until dissolved.
Add the coffee and pumpkin puree into the larger amount of batter and mix until combined.
Pour the pumpkin-coffee batter into the crust. Pour the ¾ cup of batter over the pumpkin batter and swirl them together.
Lower the oven temperature to 325?.
Bake for 60-85 minutes until the cheesecake has darkened and is not slightly jiggly (but not too jiggly).*Oven temperatures vary.
Then turn off the oven and let the cheesecake sit there for 30 minutes.
Remove the cheesecake from the oven and run a knife along the sides of the pan.
Cool completely on a wire cooling rack for 2 hours.
Cover and chill in the refrigerator for 24 hours.
Most bakers remove cheesecakes from the oven far too early because they mistake residual heat for underbaking.
Reading the Jiggle
Visual cues remain the most reliable indicator of doneness for heavy dairy batters. Gently nudge the springform pan to observe the center three inches. Proper doneness shows a firm outer ring with a slight, uniform ripple in the exact middle rather than a liquid wave. Residual thermal energy continues cooking the interior during the mandatory cooling window.
Managing Thermal Shock
Cracks form when proteins seize from sudden temperature changes or overbeating. Lowering the oven heat from 350 degrees Fahrenheit to 325 degrees halfway through prevents the outer edges from browning before the center sets. Turning off the heat entirely and leaving the dessert inside the dark oven for 30 minutes allows internal temperatures to drop gradually.
The Architecture of the Crust
Combining graham crackers with toasted pecans or hazelnuts provides structural support against heavy fillings. Processing the nuts finely with melted butter and brown sugar ensures the mixture packs tightly two inches up the sides of a 9-inch pan. Pre-baking this foundation for exactly 12 minutes prevents sogginess when the wet batter is introduced.