Melt 2 tablespoons of butter with olive oil in a 6-quart Dutch oven or heavy soup pot over medium heat. Add the diced onion, carrots, and celery. Sauté for 6 to 8 minutes until the vegetables are softened and onions become translucent.

Add the minced garlic, fresh thyme, poultry seasoning, kosher salt, and black pepper. Stir for 60 seconds until delightfully fragrant. Melt in the remaining 2 tablespoons of butter, then sprinkle in 1/3 cup of flour. Stir vigorously for 2 minutes to cook off raw flour flavor.

Slowly stream in warm chicken bone broth in steady increments while whisking continuously to form an ultra-smooth, silky gravy without lumps. Bring to a gentle boil, then lower the heat to medium-low and simmer for 10 minutes until slightly thickened. Stir in shredded chicken and heavy cream.

While the stew simmers, prepare the dumpling dough: In a medium bowl, whisk together 2 cups flour, baking powder, baking soda, and salt. Cut in the cold butter cubes using a pastry cutter or your fingertips until the mixture resembles coarse pea-sized crumbs. Gently stir in cold buttermilk and chopped parsley with a fork just until a soft, sticky dough forms (do not overmix!).

Stir frozen peas into the simmering stew. Using a standard cookie scoop or two spoons, drop golf-ball sized mounds of dumpling dough directly onto the surface of the simmering chicken stew, spacing them evenly.

Immediately cover the pot with a tight-fitting lid and reduce heat to low. Simmer undisturbed for 15 minutes without lifting the lid so the steam cooks the dumplings through. Check with a toothpick in the center of a dumpling; it should come out clean and fluffy.

Gently ladle into shallow bowls, ensuring each portion receives generous dumplings and velvety chicken gravy. Garnish with fresh cracked pepper and chopped parsley. Serve steaming hot.