Preheat the oven to 325°F / 163°C and mix graham cracker crumbs with melted butter, then press into the bottom of a 9-inch springform pan.
Beat cream cheese and sugar until smooth, then add pumpkin puree, eggs one at a time, pumpkin pie spice, and vanilla extract until fully combined.
Pour the filling over the crust and smooth the top with a spatula.
Bake for 55 to 60 minutes until the edges are set but the center still jiggles slightly when gently shaken.
Turn off the oven, crack the door open, and let the cheesecake cool inside for 1 hour to prevent cracking.
Refrigerate for at least 4 hours or overnight before removing from the pan and slicing.