In a large pot, melt 2 tablespoons of butter over medium heat. Add the diced chicken and season with salt and pepper. Cook until no longer pink (about 5-7 minutes). Remove from pot and set aside.
In the same pot, add another tablespoon of butter. Once melted, add the carrots, celery, and onion. Sauté until the vegetables are tender (about 5 minutes).
Pour in the chicken broth and add thyme. Bring the mixture to a simmer.
Stir in the heavy cream and let it simmer for an additional 10 minutes to thicken the soup. Add the cooked chicken and frozen peas.
Taste the soup for seasoning and adjust with salt and pepper as desired. If you like it thicker, you can mix 1 tablespoon of cornstarch with cold water and stir it in while simmering.
Ladle the soup into bowls and garnish with fresh parsley for a touch of color.