Cook the Chicken: In a large pot, heat the olive oil over medium heat. Add the chicken breasts or thighs and cook until browned and cooked through, about 6-8 minutes per side. Remove the chicken from the pot and set aside to cool. Once cool, shred the chicken into bite-sized pieces.

Sauté Vegetables: In the same pot, add the butter. Once melted, add the diced onion, carrots, celery, and potatoes. Cook until the vegetables are softened, about 5-7 minutes. Add the minced garlic and cook for another 1-2 minutes until fragrant.

Make the Roux: Sprinkle the flour over the vegetables and stir well to combine. Cook for 1-2 minutes to eliminate the raw flour taste.

Add Broth and Simmer: Slowly pour in the chicken broth while stirring to prevent lumps. Bring the mixture to a boil, then reduce the heat and let it simmer until the potatoes are tender, about 10-15 minutes.

Add Chicken and Cream: Stir in the shredded chicken, frozen peas, dried thyme, dried rosemary, salt, and pepper. Pour in the heavy cream and let the soup simmer for another 5-10 minutes until it thickens and all the flavors meld together.

Serve: Ladle the soup into bowls and garnish with fresh parsley. Serve with puff pastry squares or biscuits on the side for a complete meal.