Before diving in, make sure your pumpkin isn't too large. If it's much larger than the one pictured the timing of baking the pumpkin and the custard may be off; a larger, thick-walled pumpkin is an excellent insulator, which will prevent the heat from reaching the custard in the middle of the pumpkin.
Preheat oven to 375 degrees Fahrenheit and coat the bottom of a roasting pan lightly with oil (select a roasting pan large enough to hold the pumpkin and its lid, side-by-side).
Cut a lid off the pumpkin and remove the guts and seeds (save the seeds for baking later).
Once the inside of the pumpkin is cleaned out, take a fork and gently score the inside walls.
Sprinkle the inside of the pumpkin with a tablespoon of the white sugar and bake, open side down, in the roasting pan for about 30 minutes, or until just barely fork-tender (start checking at 20 minutes).
While the pumpkin bakes, break the eggs into a mixing bowl and whisk for about a minute, or until frothy.
Add to the bowl the heavy whipping cream, brown sugar, spices, vanilla extract, and salt. Whisk until thoroughly mixed.
Add the remaining white sugar to the bowl, and whisk until all ingredients are combined and the sugar is dissolved; this can take several minutes.
Pour the custard mixture into a saucepan and cook for 20 minutes over low heat, stirring often. Do not allow the custard to come to a boil. After it starts to thicken, turn off the heat.
Remove the pumpkin from the oven and turn right side up, placing back into the roasting pan. Pour the custard into the pumpkin.
Place about 1/2 inch of water into the roasting pan and place the lid, cut-side down, beside the pumpkin.
Bake the pumpkin for about an hour and a half, or until the custard sets. After an hour has passed, test the pumpkin by sticking a long cake tester or knife into the center of the custard; at this point the custard likely won't be set all the way through (but oven temperatures vary and elevation can greatly impact baking times). If the custard isn't set continue baking, testing every 15 minutes, until done. (Do not bake with the lid on the pumpkin; the pumpkin lid will prevent the custard from cooking through.)
After the custard is set, remove the pumpkin from the oven and let it cool for about 30 minutes.
Serve the pumpkin by scooping out generous helpings of custard, scraping the soft pumpkin from the sides. It's fun to bring the whole pumpkin to the table and allow everyone to serve themselves.