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Step 1
In a medium bowl, season chicken with salt and pepper and toss with 1/2 cup flour.
Step 2
Heat 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat. Add chicken and cook until outsides are browned, stirring occasionally, 3-5 minutes. Remove to a plate and set aside.
Step 3
Reduce heat to medium and add remaining olive oil and butter. Add carrots, celery, and onion and cook until softened, about 5 minutes.
Step 4
Stir in broth, thyme, bay leaves, and chicken. Bring to a simmer, then stir in cream and peas and season to taste with salt and pepper.
Step 5
Meanwhile, prepare the dumplings:
Step 6
In a medium bowl, stir together the 1 1/2 cups flour, baking powder, and salt. Add buttermilk and eggs and stir until no raw flour remains.
Step 7
Drop dough by tablespoons into simmering broth, giving them some space to puff up.
Step 8
Cover, reduce heat, and let simmer gently until dumplings are puffy and chicken has cooked through, about 15 minutes. Enjoy!