Make the crust: Mix graham cracker crumbs, melted butter, and sugar until it looks like wet sand. Press firmly into the bottom of a 9-inch springform pan and bake at 325°F for 8 minutes.
Beat the cream cheese: In a large bowl, beat softened cream cheese with both sugars until smooth and fluffy, about 3 minutes. Scrape down the bowl so no lumps remain.
Add pumpkin and spices: Mix in pumpkin puree, sour cream, flour, pumpkin pie spice, cinnamon, and vanilla on low speed until just combined. Avoid overmixing to keep air bubbles to a minimum.
Mix in the eggs: Add eggs one at a time, beating on low just until the yellow disappears after each one. Stop mixing as soon as the batter looks smooth and uniform.
Pour over the crust: Pour the filling over the baked crust and smooth the top with a spatula. Tap the pan gently on the counter a few times to release any large air bubbles.
Wrap for the water bath: Wrap the outside of the springform pan tightly in two layers of heavy-duty foil. Place it inside a larger roasting pan.
Add hot water: Pour hot water into the roasting pan until it reaches halfway up the sides of the springform pan. This gentle, moist heat prevents the filling from drying out or cracking.
Bake low and slow: Bake at 325°F for 60 to 70 minutes, until the edges look set and puffed slightly but the center still jiggles like soft custard when the pan is nudged.
Cool gradually in the oven: Turn off the oven and crack the door open, letting the cheesecake sit inside for 1 hour. This slow cooling prevents sudden temperature shock, which causes cracks on the surface.
Chill completely: Remove the cheesecake from the water bath, let it cool to room temperature, then refrigerate uncovered for at least 6 hours or overnight until fully set.
Make the streusel: Mix flour, brown sugar, and cinnamon, then cut in cold butter with your fingers until it forms small clumps. Stir in the chopped pecans.
Toast the streusel: Spread the streusel mixture on a baking sheet and toast at 350°F for 8 to 10 minutes, until golden and fragrant. Let it cool completely before using.
Top and slice: Sprinkle the cooled pecan streusel over the chilled cheesecake just before serving. Slice with a warm, dry knife, wiping it clean between cuts for neat slices.