Cut a circle around the top of the pumpkin, just like you would for a jack-o'-lantern, and lift off the lid. Use your sturdy spoon to scrape out all the seeds and stringy fibers until the inside walls are clean. Rub the inside generously with olive oil, then season with half your salt, some pepper, and a bit of minced garlic.
Place the hollowed pumpkin on a baking sheet, replace the lid, and roast it at 350°F for about 30 minutes. This head start softens the flesh and cuts down on your overall cooking time, so the pumpkin and filling finish cooking at roughly the same pace.
While the pumpkin roasts, cook your ground beef in a large skillet over medium heat until no pink remains. Drain any excess fat, then stir in the garlic, oregano, and remaining salt so the seasoning has time to bloom in the warm meat.
Transfer the cooked beef to your mixing bowl and add the rice, tomato sauce, ham if using, eggs, and apple cider vinegar. Stir gently until everything is evenly combined, being careful not to overmix, which can make the texture dense.
Remove the precooked pumpkin from the oven and pack the filling firmly inside, pressing down as you go so there are no air pockets. Sprinkle your shredded cheese over the top, replace the lid, and bake uncovered at 350°F for about an hour, or until the pumpkin flesh is fork-tender.
Let the whole pumpkin rest for about 10 minutes once it comes out of the oven. This gives the filling a chance to set slightly, which makes slicing into clean wedges much easier at the table.