Add the oil and mirepoix to a large stockpot over medium heat. Sauté until the onion, carrot, and celery have softened.
3 Cups Mirepoix, 3 Tbsp Cooking Oil
Add the chicken backs to the pot. Pour in about 8 cups of water, or enough to cover the chicken.
2 Chicken Backs, 8 Cups Water
Bring the water to a boil over medium-high heat. Reduce to a steady simmer, cover, and cook for 20 minutes.
Remove the chicken from the pot. Carefully remove and discard the skin, which should slip off fairly easily. Separate the bones from the meat, then cut the chicken into smaller pieces. Some of the meat may be partially cooked while some may still be raw at this point.
Return the chicken meat and the large intact bones separately to the stockpot. Simmer for another 20 minutes.
Remove and discard all of the chicken bones before adding the remaining vegetables.
Wash the potatoes well, peel if desired, and cut them into roughly 1-inch cubes.
2½ Cups Potatoes
Wash the delicata squash, cut it in half lengthwise, and scoop out the seeds and stringy centre with a spoon. Cut the squash into smaller sections before peeling so it is easier to handle, then carefully remove the skin with a vegetable peeler or paring knife. Cut the peeled squash into roughly 1-inch cubes. Delicata can be awkward to peel because of its ridged shape, so butternut squash can be used instead if you prefer an easier squash to prepare.
Place the celery leaves in a colander and rinse them very well under cool running water, tossing the leaves with your hands so the water reaches both sides. Wash the Swiss chard thoroughly as well, paying attention to the leaves and around the stems.
1 Cup Fresh Celery Leaves, 4 Cups Rainbow Swiss Chard
Add the celery leaves, Swiss chard, delicata squash, potatoes, and dried oregano. Season with salt and black pepper.
4 Cups Delicata Squash, 1 Tsp Dried Oregano, Salt, Black Pepper
Cover and simmer gently for about 1 hour, stirring occasionally, until the potatoes are tender and the delicata squash is very soft. Some of the squash should begin to break down into the broth.
Taste the soup and adjust the salt and black pepper as needed.
Serve hot with fresh bread, rolls, biscuits, or toast.