In a medium soup pot, set over medium heat, heat the oil. Once the oil is hot, but not smoking, add the shallot, celery and carrots. Next, mix in the fresh thyme sprigs. Cook until the vegetables are softened, about 3 minutes.
Pour in the water and chicken broth. Place the chicken carcass (shredded chicken removed) in the center of the pot. Bring to a simmer and cover the pot. Cook for 15-20 minutes or until very fragrant.
Meanwhile, make the dumplings. In a medium bowl, whisk together the flour, baking powder and salt. Add the buttermilk and mix until just combined.
Remove the carcass from the broth water and discard. At this time the broth should be flavorful and fragrant. Give it a taste and adjust the seasonings according to your liking. I added a heavy pinch of salt. Depending on the rotisserie chicken you're using, you may need to skim the top of the broth to remove some of the fat. Adrianna (and I) prefer to leave the fat, as it adds great flavor!
Bring the broth to a medium boil. Drop a heaping tablespoon of the dough into the boiling point (the extreme heat from the bubbling point reacts with the baking powder in the dough to create a really fluffy dumpling). Continue until you've worked your way through all the dough. You should end up with 10-12 dumplings. Cover the pot so the dumplings can cook for about 2-3 minutes.
Carefully move the dumplings aside and slide the shredded chicken into the broth and allow to heat. Next, divide the dumplings and broth between 4 bowls and serve with a sprinkle of black pepper and parmesan cheese (if desired)
*Adapted with permission from [The Year Of Cozy | http://www.amazon.com/The-Year-Cozy-Homemade-Adventures/dp/1623365104] by Adrianna Adarme.