1. Preheat barbecue to 425 degrees for indirect heating.
2. Prepare your pie crust and set aside. You can either use a pre-made one or try making your own from scratch.
3. To prepare the pumpkin puree, cut off the top of the pumpkin and scrape out all the seeds and membrane (a large metal serving spoon works well) and then carefully cut it into sections with a paring knife. Cut the skin off the flesh and steam flesh until tender. Then puree in a food processor or blender until smooth.
4. Combine pumpkin puree, beaten eggs, ginger, cinnamon, nutmeg and ground cloves in a bowl and stir. It's okay if there are a few lumps ... those will bake out. Add the flour, white sugar and brown sugar to the pumpkin mixture and mix together. Next, add the heavy cream and stir.
5. Pour filling into an unbaked pie crust. Bake pie in barbecue over indirect heat for 15 minutes. Open vents or crack lid if using charcoal, or turn down the burners if using gas to lower the temperature to 350 degrees and bake for 45 minutes longer, or until a knife inserted in the center comes out clean. Cool completely. Keep refrigerated.
6. Serve with a dollop of sweetened whipped cream, if desired.
Tip: To help prevent the pie crust from becoming soggy in a custard-style pie, break one of the recipe's eggs into unbaked pie crust, swish it around to cover entire surface with egg white and then pour the egg out into your mixing bowl for the filling. Do NOT boil pumpkin – it will soak up the water and make a watery pie.