Sauté the aromatics: In a large heavy pot, heat olive oil and butter over medium heat. Add onion, carrots, and celery with a pinch of salt. Cook 6–8 minutes, stirring, until softened. Add garlic, thyme, and bay leaf; cook 1 minute until fragrant.

Build the base: Sprinkle 1/3 cup flour over the vegetables. Stir for 1–2 minutes to cook off the raw flour taste. Gradually whisk in chicken stock until smooth.

Simmer the chicken: Add chicken thighs and breasts. Bring to a gentle simmer, then reduce heat to low. Cover and cook 15–20 minutes, until the chicken is just cooked through and tender.

Shred and season: Transfer chicken to a plate. Shred into bite-size pieces with two forks. Fish out the bay leaf. Taste the broth and adjust salt and pepper.

Add cream and herbs: Stir in heavy cream, parsley, and dill. Return shredded chicken to the pot. Keep at a very gentle simmer. You want steam and tiny bubbles, not a rolling boil.

Make the dumpling dough: In a bowl, whisk flour, baking powder, baking soda, salt, and garlic powder. Cut in cold butter with your fingers until it resembles coarse crumbs. Stir in buttermilk and chives until just combined. The dough should be thick and slightly sticky. Do not overmix.

Drop the dumplings: Using a small cookie scoop or two spoons, drop tablespoon-sized mounds onto the simmering broth, spacing them slightly. They’ll puff as they cook.

Cover and steam: Cover the pot tightly and cook 12–15 minutes at a gentle simmer. Avoid lifting the lid in the first 10 minutes. The dumplings are done when puffed and firm on the outside and cooked through in the center.

Finish and brighten: Stir in lemon juice for a fresh lift. Taste and adjust seasoning. If the broth is too thick, splash in a little extra stock or water; if too thin, simmer uncovered 2–3 minutes.

Serve: Ladle broth, chicken, and dumplings into warm bowls. Garnish with extra parsley or chives.