In a large Dutch oven or heavy-bottomed pot, melt 4 tablespoons of butter over medium heat. Add the chopped onion, carrots, and celery. Sauté for 6-8 minutes until softened. Add the minced garlic and fresh thyme sprigs and cook for one more minute until fragrant.

Sprinkle 1/3 cup of all-purpose flour over the vegetables and stir continuously for one minute to cook out the raw flour taste. Slowly whisk in the low-sodium chicken broth until smooth, then stir in the heavy cream. Bring the mixture to a gentle simmer, then reduce heat to low.

While the soup simmers, prepare the dumpling dough. In a medium bowl, whisk together 2 cups of flour, baking powder, sugar, and 1 teaspoon of salt. Add the cold, cubed butter and use a pastry blender or your fingertips to cut it in until the mixture resembles coarse crumbs.

Pour in the cold buttermilk and stir with a fork until just combined. Do not overmix; the dough should be shaggy and slightly sticky.

Add the shredded rotisserie chicken to the simmering soup base. Season with salt and black pepper to taste. Increase the heat slightly to maintain a steady, gentle simmer.

Using two spoons or a small cookie scoop, drop rounded tablespoons of the dumpling dough into the simmering soup, spacing them evenly. Immediately cover the pot with a tight-fitting lid, reduce the heat to low, and let the dumplings steam for 15-18 minutes. Do not lift the lid.

After 15-18 minutes, remove the lid. The dumplings should be puffed and cooked through (a toothpick inserted into the center should come out clean). Gently stir in the fresh chopped parsley. Ladle into bowls and serve immediately.