Season the chicken with salt and black pepper and toss with ½ cup of all-purpose flour.
Heat a tablespoon of oil in a Dutch oven or large pan over a moderate to high heat.
Add the chicken and sear for 4 minutes or until golden all over.
Transfer to a plate and set to one side.
Turn down the heat and add the butter and rest of the oil.
Add the vegetables and cook for 5 minutes or until soft.
Stir in the broth, chicken and herbs, and bring the mixture to a simmer.
Add the peas and cream and adjust the seasoning if needed.
While that is cooking, you can prepare the dumplings.
Mix the flour with the baking powder and salt.
Add the eggs and buttermilk and mix well.
Drop spoonfuls of this dumpling mixture into the simmering soup, allowing space for them to get puffy.
Cover the pot, turn the heat down and simmer 15 minutes or until the chicken is cooked through and the dumplings are puffed up.