In a large pot, heat 2 tablespoons of olive oil over medium heat. Once the oil shimmers, add the diced onion and sauté for about 3 minutes until translucent. Then, add the minced garlic and continue cooking for another minute, stirring frequently, until fragrant.

Add the diced carrots and celery to the pot, stirring well. Sauté the mixture for 5-7 minutes until the vegetables soften and start to caramelize slightly.

Stir in the shredded chicken breast, allowing it to warm up for a minute. Then, pour in 4 cups of low-sodium chicken broth and add 1 cup of frozen peas, as well as the dried thyme and rosemary. Bring the mixture to a gentle simmer over medium-high heat, allowing the flavors to meld for about 10 minutes.

In a small bowl, whisk together 1/4 cup of all-purpose flour and 1 cup of heavy cream or milk until smooth. This mixture will help thicken your soup, giving it a creamy texture.

Gradually add the flour and cream mixture to the pot while stirring continuously to prevent lumps from forming. Maintain a gentle simmer and cook for an additional 10-15 minutes, stirring frequently until the soup thickens to your desired consistency. Taste and adjust seasoning with salt and pepper as needed.

Once the soup has reached a rich, creamy texture, remove it from heat. Allow the soup to sit for a few minutes to allow the flavors to deepen.

Ladle the warm soup into bowls and garnish each serving with freshly chopped parsley. Pair it with crusty bread or homemade biscuits for a complete meal.