Preheat the oven to 400 degrees F (200 degrees C). Line a large baking sheet with aluminum foil.

Arrange squash on the prepared baking sheet.

Cook in the preheated oven until skin is browned and flesh is tender, about 45 minutes; cool before handling. Remove flesh from squash using a spoon.

Reduce the oven temperature to 375 degrees F (190 degrees C).

Place 2 cups squash flesh in the bowl of a food processor; pulse until smooth. Add eggs, brown sugar, cream, butter, apple pie spice, and salt; pulse until smooth. Pour squash filling into pie crust.

Bake in the preheated oven until filling rises, about 1 hour.