In a large pot, heat 1 tablespoon of olive oil over medium-high heat. Brown the chicken on all sides (avoid stirring until browned on the bottom). Remove to a large bowl and set aside.
Add the remaining olive oil. Add the onion, garlic, carrots, and celery. Cook for 4-5 minutes until softened.
Stir in the flour until evenly mixed throughout.
Add the chicken broth, Italian seasoning, ground thyme, and potatoes. Bring to a boil, reduce to a simmer, then cover and cook for 20 minutes until the potatoes are tender.
Stir in the frozen peas, heavy cream, and chicken, and cook for 2 more minutes. Season with salt and pepper to taste (start with ½ teaspoon of each and then add more if you like)