Preheat oven to 375 degrees F. However, if you need to pre-bake the crust, increase heat to 425 degrees F. Carefully line the pie crust with parchment or foil, and put dried beans or rice (something to weigh it down) on top. Bake for 12-15 minutes. Remove from oven and discard the parchment.
Roughly chop the peeled carrots, place them in a large saucepan, and cover with 1 inch of water. Bring to a boil over high heat, cover, and then reduce heat to medium. Cook for 12-15 minutes or until the carrots are tender. Drain the excess water in the pan and return it (with the carrots) to the stove. Turn the heat back on to medium and let the carrots cook for a few minutes to "steam" off any excess moisture.
Add the cooked carrots, heavy cream, maple syrup, eggs, vanilla, cinnamon, allspice, ginger, and salt to a blender or food processor. Blend until smooth, about 1 minute. Pour the filling in the pie crust. If desired, cover the edges of the crust with a little foil to avoid burnt edges.
Bake for 50-65 minutes (at 375 F), or until the center of the pie no longer "jiggles" and a toothpick inserted in the center comes out clean. The top of the pie should be slightly caramelized.
Remove from oven and let it cool for 30 minutes at room temp before putting it in the fridge for another 60 minutes to finish cooling. Slice with a sharp knife, and serve with whipped cream!