In a large pot, melt the butter over medium heat. Add the onion, garlic, carrots, and celery. Cook for 4-5 minutes until softened.
Stir in the flour until mixed throughout the veggies.
While whisking constantly, pour in the chicken broth. Bring to a boil, then reduce to a simmer, and cook for 2 minutes.
Stir in the cream, chicken, peas, thyme, salt, and pepper. Bring to a boil again, then let it gently simmer while you prepare the dumplings.
In a medium mixing bowl, whisk the flour, baking powder, and salt together. Stir in the milk and olive oil until just combined- do not overmix!
While the soup is simmering, drop spoonfuls of dough into the soup. To prevent sticking, dip your spoon in the hot soup between each spoonful. Reduce the heat to a simmer, cover, and cook for 10-12 minutes.
To check for doneness, insert a toothpick into the dumpling. If it comes out clean, it's ready. Otherwise, cook for a few more minutes.