1. To make the crust, heat the oven to 350 degrees. Combine the sugar and graham cracker pieces in the bowl of a food processor and process until they're finely ground. You should have about 1 1/2 cups; add or remove some if not. Slowly add the butter and pulse a few times until they're all moistened by the butter (if the crumbs aren't all moistened, add a little bit more melted butter). Press the crumbs evenly into the bottom and sides of a pie plate.
2. Bake the crust for 8 to 10 minutes, just until it begins to brown. Set the pie plate on a rack; the crust will crisp as it cools. Turn the oven up to 375.
3. While the crust is baking, use an electric mixer or a whisk to beat the eggs with the sugar, then add the cinnamon, ginger, nutmeg, cloves and salt. Add the pumpkin puree, mix, then add the half and half.
4. Put the pie plate with the crust on a rimmed baking sheet. Pour the pumpkin mixture into the crust all the way to the top (you might have some left over). Transfer the whole baking sheet to the oven (in case of spillover) and bake for 30 to 40 minutes, until the mixture shakes like Jell-O but is still quite moist in the center. Cool on a rack until it no longer giggles, then slice into wedges and serve, or refrigerate for a day or two.
For the fresh pumpkin puree:
1. Cut a circle around the stem of the pumpkin, then pull off on the stem and discard it. Use the cavity as a handle and peel the pumpkin with a vegetable peeler. Using a sharp and sturdy knife, cut the pumpkin in half and scrape out the seeds with an ice cream scoop or heavy spoon. Cut or scrape off any excess string and cut the pumpkin into 1-inch cubes.
2. Bring a large pot of water to a boil and add the pumpkin; boil until soft, 15 to 20 minutes. Drain the pumpkin and puree until smooth in a blender or food processor.