In a spacious pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until it becomes translucent and fragrant.
Incorporate the minced garlic, diced carrots, and celery into the pot. Continue to cook for an additional 5-7 minutes, stirring occasionally, until the vegetables soften and become tender.
Add the shredded chicken into the pot, stirring to combine and ensuring it warms through evenly.
Sprinkle the all-purpose flour over the chicken and vegetable mixture, stirring well to coat everything. Allow it to cook for about 1 minute; this will help eliminate any raw flour taste.
Gradually pour in the chicken broth while continuously stirring to avoid any lumps from forming.
Bring the mixture to a gentle boil. Once boiling, reduce the heat slightly and let it simmer for about 10 minutes, allowing the flavors to meld beautifully.
Lower the heat to a gentle simmer and stir in the heavy cream, frozen peas, dried thyme, dried rosemary, and season with salt and pepper to taste. Allow the soup to simmer for an additional 5 minutes until the peas are bright and heated through.
While the soup is simmering, preheat your oven to 400°F (200°C). Roll out the thawed puff pastry sheets and cut them into circles large enough to cover the soup bowls.
Ladle the delicious soup into individual oven-safe bowls. Place a puff pastry round on top of each bowl. Make a few small slits in the pastry to allow steam to escape during baking.
Transfer the bowls to the preheated oven and bake for 15-20 minutes or until the puff pastry is golden brown and puffy, creating a delightful crust.
Notes
Serve hot with fresh parsley garnish for added flavor.