Melt the butter in a large pot over medium heat. Add the chicken pieces and cook until lightly browned on all sides.
Add the onion, carrots, celery, and garlic. Stir and cook for several minutes until the vegetables begin to soften.
Stir in the potatoes, chicken broth, thyme, salt, and pepper. Bring the mixture to a boil, then reduce the heat and simmer until the potatoes are tender.
Sprinkle the flour over the stew and stir well to thicken the broth.
Pour in the heavy cream and add the frozen peas. Simmer gently for a few more minutes until the peas are heated through and the stew reaches a creamy consistency.
Remove from heat and stir in the fresh parsley before serving.