Preheat oven to 400 degrees F (200 degrees C). Place crust into a pie plate.
Combine pumpkin, heavy cream, brown sugar, eggs, rum, pumpkin spice, and salt in a large bowl. Stir until smooth. Pour mixture into the crust.
Bake in the preheated oven for 15 minutes. Reduce oven temperature to 350 degrees F (175 degrees C). Continue baking until a knife inserted into the center comes out clean, about 40 minutes more. Allow to cool.