Prepare the pumpkin - wash, cut a lid in the top, clean out the seeds and the stringy pulp.
Place the chicken pieces at the bottom of the pumpkin. Layer on top of the chicken the kosher salt, ground pepper, smashed garlic cloves, chicken base, chopped carrots, chopped potatoes, chopped leek, chopped shallots, chopped onion, bay leaves, lemon peel and sprigs of fresh thyme. Drizzle everything inside liberally with olive oil.
Place the top back on the pumpkin. Coat the outside of the pumpkin with olive oil and then place the pumpkin in a large high-sided baking dish or cast-iron skillet.
Bake for 2 ½ - 3 hours, until the pumpkin is very tender; the pumpkin skin is very dark; and, the broth is at the top of the pumpkin cavity.
Remove lemon peel, thyme sprigs and bay leaf before serving.
Scoop out soup, chicken and some of the pumpkin from the inside into a bowl and serve. Season with salt to taste.
Video
Notes
A shorter, rounder large pumpkin works best so that it fits well in the oven.
The broth doesn't start to produce in the pumpkin until the pumpkin has been in the oven for at least 2 hours.
You can use boneless chicken BUT keep in mind the bone-in, skin-on chicken provides much more flavor.