Heat the olive oil in a large Dutch oven over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes. Remove the chicken to a plate and set aside.
Add the onion, carrots, celery, and mushrooms to the pot. Cook for 6 minutes until the vegetables soften and the mushrooms release their liquid.
Stir in the garlic and cook for 1 minute. Sprinkle the flour over the vegetables and stir for another minute to coat everything evenly.
Slowly pour in the chicken broth while stirring to avoid lumps. Add the diced potatoes, thyme, salt, and pepper. Return the chicken to the pot.
Bring the mixture to a simmer, then reduce the heat to low. Cover and cook for 20 minutes until the potatoes are tender.
Stir in the heavy cream and simmer uncovered for 5 more minutes. Taste and adjust salt or pepper if needed. Sprinkle with fresh parsley before serving.