Heat oil over medium heat in heavy-bottomed pot such as a Dutch oven.
Add onions and garlic. Cook, stirring frequently until onions are softened, about 3 minutes.
Add carrots and celery. Cook, stirring frequently to avoid browning, for about 5 minutes.
Add basil, thyme and flour. Stir for about 1 minute. Then slowly stir in water/broth/stock and salt. Turn heat to high and cover. Stir occasionally until the mixture reaches a boil.
Reduce heat to maintain a steady simmering with lid on, stirring occasionally. Cook for 10 minutes.
Prepare the dumplings while the pot simmers. Dumplings: Sift flour, baking powder and salt. Cut in butter until butter is about the size of peas. Then gently add the milk, being careful not to overmix.
Stir in potatoes, then drop dumplings on top, about a 1/4 cup in size. Return to a simmer and cook another 10 minutes or until potatoes are fork tender.
Reduce heat to low and add peas and chicken. Gently stir these in between the dumplings. Cover and cook about 3 minutes or until peas are tender and chicken is heated through.
Add additional salt/pepper if needed. Enjoy!