Preheat oven to 400 degrees F (200 degrees C). Line a large baking sheet with aluminum foil.
Arrange squash on lined baking sheet. Roast in preheated oven until the skin is browned and flesh is tender, about 45 minutes; allow to cool before handling.
Remove flesh from squash using a spoon.
Reduce temperature setting on oven to 375 degrees F (190 degrees C).
Place 2 cups of squash in a food processor and process until smooth.
Add the brown sugar, eggs, cream, apple pie spice, salt, and butter; process until smooth.
Pour the squash mixture into the pie crust. Bake until the filling rises, about 1 hour.