In a large pot or Dutch oven, heat the olive oil over medium heat.
Add the onion, celery, and carrots and cook until the vegetables are tender, about 5 to 7 minutes.
Add in the garlic, salt, and pepper and cook for an additional minute.
Place the chicken breasts in the pot and pour in the chicken broth.
Add the bay leaves and thyme. Bring the mixture to a boil, then reduce the heat to low and simmer until the chicken is cooked through, about 15 minutes.
Meanwhile, prepare the dumpling dough. In a separate bowl, whisk together the flour, baking powder, and salt. Gradually stir in the buttermilk to form a soft dough.
Turn the dough out on a floured surface and, using a rolling pin, roll the dough to about 1/4- inch thickness. Cut into 1 inch-thick strips. Cut each of those strips into pieces that are approximately 2 inches in length.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the pot.
In a small bowl, whisk together the heavy cream and flour until smooth. Stir the mixture into the soup. Bring the soup to a boil.
Drop the prepared dumpling dough into the boiling soup. Reduce the heat to low and simmer, uncovered, for 10 to 15 minutes or until the dumplings are cooked through.
Serve the soup hot and enjoy!