Melt butter in a large pot over medium heat. Add onion, carrots, and celery. Sauté until softened, about 5 minutes.
Add garlic and cook for 1 minute until fragrant.
Sprinkle flour over the vegetables and stir until coated. Cook for 2 minutes to remove the raw taste of the flour.
Gradually whisk in chicken broth, ensuring no lumps remain. Bring to a simmer.
Stir in heavy cream, shredded chicken, peas, thyme, salt, and pepper. Simmer for 10 minutes until the soup thickens.
Serve warm with optional puff pastry rounds for a pot pie-inspired finish.