Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil and arrange squash chunks, flesh-side up, on the baking sheet.
Whisk butter, 3 tablespoons brown sugar, and orange juice together in a bowl until smooth; pour over squash and toss to coat.
Bake in the preheated oven until the skin is blistery and flesh is tender, about 45 minutes. Scrape flesh from the skin, discarding skin. Blend flesh in the food processor until smooth. Measure 2 cup squash puree, reserving the rest for another use.
Lower oven temperature to 375 degrees F (190 degrees C) and move lowest rack to lowest possible position.
Blend 2 cups squash puree, eggs, 1/2 cup brown sugar, cream, allspice, cinnamon, ginger, and salt in a blender or using a whisk until mixture is smooth. Press pie crust into a pie plate and pour squash mixture into crust.
Bake in the preheated oven until pie is puffed with a small wet spot in the center, 50 to 60 minutes.