01 - Heat olive oil in a large Dutch oven or heavy pot over medium heat. Add onion, carrots, and celery; sauté 5 minutes until softened. Add garlic; cook 1 minute more.
02 - Add chicken, chicken broth, bay leaf, thyme, salt, and pepper. Bring to a boil, then reduce heat and simmer uncovered for 20–25 minutes, until chicken is cooked through.
03 - Remove chicken from the pot and shred with two forks. Discard bay leaf. Return shredded chicken to the pot. Stir in heavy cream and parsley. Keep at a gentle simmer.
04 - In a large bowl, whisk together flour, baking powder, baking soda, and salt. Cut in cold butter with a pastry blender or fingers until mixture resembles coarse crumbs. Add cold buttermilk, stirring just until dough comes together. Do not overmix.
05 - Drop tablespoon-sized mounds of dough onto the simmering soup, spacing them apart. Cover the pot tightly and simmer on low (do not lift lid) for 15 minutes, until dumplings are puffed up and cooked through.
06 - Uncover, taste broth, and adjust seasoning if needed. Serve hot, garnished with extra parsley.