Gently lay the rolled-out pie crust in a 10-inch (25-cm) pie dish. Trim the excess dough around the sides.
Tuck the dough under the edge, and crimp the edges using the index finger knuckle on one hand and the thumb and index finger on your other hand. Chill in the refrigerator for 14-20 minutes.
Make the filling: Add the pumpkin puree, cinnamon, allspice, cloves, ginger, nutmeg, and salt to a medium bowl and mix until combined.
Spread the pumpkin puree mixture onto a baking sheet in an even layer. Bake for 12-15 minutes, until it looks slightly dried out.
Increase the oven temperature to 400˚F (200˚C).
Scrape the puree into a large bowl and add the granulated sugar, dark brown sugar, vanilla, eggs, egg yolk, and half-and-half. Whisk until smooth and well combined.
After chilling the crust, crumple a piece of parchment paper, then spread it out in the center of the crust. Add dried chickpeas or baking beans to the center and spread toward the sides of the crust--this will add weight to keep the crust from puffing up and hold up the walls.
Bake the crust for 15-20 minutes, until slightly golden and there are no raw doughy spots.
Increase the oven temperature to 425˚F (220˚C).
Pour the filling into the prebaked crust. Brush the edges of the crust with egg wash.
Bake the pie for 15 minutes, then reduce the oven temperature to 350˚F (180˚C) and continue to bake for 30-35 minutes more, until the edges are set but the center still jiggles slightly when shaken.
Let cool at room temp for at least 2 hours, or in the fridge overnight.