Combine graham cracker crumbs and sugar in a bowl, then pour in melted butter and mix until the crumbs are evenly coated and resemble wet sand.
Press the crumb mixture firmly into the bottom of an 8-inch springform pan to create an even crust layer. Bake in a preheated 350°F oven for 10 minutes to set the crust, then remove and cool slightly.
In a large bowl, beat the softened cream cheese with a hand or stand mixer until smooth and creamy, about 2-3 minutes, while listening for a gentle flicking sound as it blends.
Add the pumpkin puree and half a cup of sugar to the cream cheese, mixing until fully combined and the mixture appears smooth with no lumps.
One at a time, beat in the eggs, mixing just until each is incorporated before adding the next, until the filling is silky and slightly airy.
In a small bowl, whisk together cinnamon, nutmeg, ginger, allspice, and salt, then fold these spices into the pumpkin filling to evenly distribute the warm flavors.
Pour the filling into the cooled crust, smoothing the top with a spatula to create an even surface—listen for the gentle settle and see the smooth, shiny top form.
Place the springform pan on a baking sheet to catch any potential drips and bake at 350°F for about 60 minutes, until the edges are set and the center gently jiggles when tapped.
Once baked, turn off the oven, crack the door open slightly, and let the cheesecake cool inside for 1 hour—this prevents cracks and helps it set gradually.
Remove the cheesecake from the oven, run a thin knife around the edge to loosen, then chill in the refrigerator for at least 4 hours or overnight for the best texture.
Serve the cheesecake chilled, optionally garnished with a sprinkle of cinnamon or a dollop of whipped cream for a finishing touch.
