Preheat the oven to 325°F. Grease a 9-inch springform pan.
In a large bowl, beat the cream cheese, sugar, and vanilla together until smooth and creamy. Add the eggs one at a time, mixing well after each addition.
Stir in the pumpkin puree and pumpkin pie spice.
In a separate bowl, combine the pistachios, flour, brown sugar, and melted butter until crumbly.
Press the pistachio crumble mixture into the bottom of the prepared pan.
Pour the cheesecake filling over the crust.
Bake for 35-40 minutes or until the cheesecake is set but the center is still slightly jiggly.
Remove the cheesecake from the oven and let it cool to room temperature.
Sprinkle the toffee bits over the top of the cheesecake.