Preheat the oven to 400 degrees F (200 degrees C).
Halve and clean the Butternut Squash (1) rub the flesh lightly with olive oil, and bake in preheated oven on a parchment-lined baking sheet, until very soft, about an hour, but start checking after 45 minutes.
Make the dough. In a large bowl, whisk All-Purpose Flour (2 1/2 cup), Granulated Sugar (2 tablespoon), and Salt (1/2 teaspoon) together.
Cut Unsalted Butter (1 cup) into flour and using the back of a fork or pastry cutter, incorporate butter into flour mixture until butter is in small pieces. Add Ice Water (5 fluid ounce) (1cup + 2 Tbsp) and continue to stir with fork until mixture comes together. If using a food processor, pulse at 1-second intervals until butter is the size of peas.
Add more ice water if necessary, one tablespoon at a time. Gently form mass into a ball, divide in half, and flatten each half into a disc.
If you are making a pie immediately, roll out one disc, place in a 9-inch pie dish and chill until ready to use. Wrap remaining disk in plastic wrap and refrigerate or freeze until ready to use.
When squash is cool enough to handle, scoop out the flesh and add the Heavy Cream (1 1/2 cup), Egg (3), Granulated Sugar (3/4 cup), Ground Cinnamon (1 teaspoon), Ground Ginger (1/2 teaspoon), Salt (1/2 teaspoon), Ground Nutmeg (1/2 teaspoon), and Ground Cloves (1/8 teaspoon) and pulse.
Meanwhile, blind bake the crust. Lay a sheet of parchment over pie dough, fill it with pie weights or dried beans, and bake in 400 degrees F (200 degrees C) oven for 15 minutes.
Remove parchment and beans and bake for 5-10 more minutes until just barely golden.
Add squash mixture to shell and bake at 375 degrees F (190 degrees C) for 40 to 60 minutes, depending on your oven and how much squash puree you ended up using, until the center is barely set.
Check after 20 minutes, and if it looks as though the crust is browning too quickly, reduce the temperature to 350 degrees F (180 degrees C). Let cool completely before serving.
Slice and serve once cooled.