Step 1: In a large Dutch oven or pot, heat the olive oil over medium heat. Add the chopped onion, diced carrots, and diced celery. Sauté for 5-7 minutes until the vegetables start to soften.
Step 2: Stir in the minced garlic, dried thyme, and dried rosemary. Cook for 1 minute until fragrant.
Step 3: Sprinkle the all-purpose flour over the vegetables. Cook, stirring constantly, for 2 minutes to create a roux.
Step 4: Gradually whisk in the chicken broth, then the milk and heavy cream, ensuring no lumps form. Bring the soup to a gentle simmer, stirring occasionally, until it begins to thicken, about 5-7 minutes.
Step 5: Add the cooked shredded chicken, frozen peas, and frozen corn to the pot. Stir to combine.
Step 6: Continue to simmer for another 5-10 minutes, or until the vegetables are tender and the soup is heated through.
Step 7: Season generously with salt and freshly ground black pepper to taste. Ladle into bowls, garnish with fresh parsley if desired, and serve warm.