Pulse the Graham-style crackers in a food processor until finely ground.
Combine the cracker crumbs, pumpkin spice, and melted butter in a mixing bowl.
Firmly press the crumb mixture over the bottom and up the sides of a 23 cm springform pan or cake ring. Refrigerate for at least 15 minutes to set.
Spiced pumpkin filling
Preheat the oven to 160°C.
Blend the cream cheese, pumpkin purée, whole eggs, egg yolks, brown sugar, cornstarch, salt, and pumpkin spice until smooth.
Pour the filling into the crust, stopping just below the rim of the cake ring. If you like, remove any bubbles with a kitchen torch, though it’s not essential.
Baking and cooling
Bake for 55 minutes to 1 hour. Gently shake the pan; the filling should still jiggle slightly in the center.
Remove the cheesecake from the oven and let it cool for about 1 hour, or until close to room temperature.
Refrigerate the cheesecake for at least 4 hours or overnight before slicing and serving.
Note: Do not refrigerate the cheesecake while it is still warm or hot.