Place a large pot or Dutch oven over medium-high heat. Once the oil is sizzling, season the chicken with salt and pepper on both sides and add it to the pot. Brown on each side for about 5-7 minutes. The chicken doesn't have to be fully cooked, but nicely browned for extra flavor.
Next, remove chicken from the pot and set it aside on a plate, cover with foil.
Add three tablespoons of butter to the same pot and melt. Add onion, stir and cook for 1 minute. Add minced garlic, shredded carrots, and celery. Stir and cook until softened for about 5 minutes.
Add 1/3 of flour and stir to combine. Stir and cook for 1-2 minutes. Add cream little by little and stir very well until combined.
Add chicken broth, dried parsley, and basil. Add salt and pepper. Stir to combine.
Add back chicken breasts, bring to a boil. Reduce heat to low and simmer covered for 10 minutes.
Once the chicken is cooked, transfer the chicken breast to a large bowl, and use forks to shred it.
Add salt and pepper to taste.
Add flour, salt, and baking powder to a medium bowl. Stir to combine.
Add melted butter, and using a fork stir it until combined and a crumbly mixture forms.
Add buttermilk and stir until fully combined.
ADD THE DUMPLINGS:
Add the shredded chicken. Use a small cookie scoop, about 1 tablespoon in size. Use a larger spoon, for larger dumplings. Scoop dough and drop directly into the simmering soup. Place them around the pot, not all in the same place.
Once all dumplings have been added, gently press them down so the soup covers them. Add the frozen peas.
Cover with the lid and continue to cook on low heat for about 15 minutes. Gently stir from time to time, to make sure stuff doesn't stick to the bottom of the pot.
Once the dumplings are cooked through garnish with fresh parsley and serve.
You can use a shredded rotisserie chicken to save time. You can also use biscuit dough, instead of the homemade dumplings.