In a large pot or Dutch oven, melt butter over medium heat. Add onion, carrots, and celery. Cook for 5-6 minutes until vegetables begin to soften. Add garlic and cook for 1 minute more until fragrant.

Sprinkle flour over the vegetables and stir constantly for 1-2 minutes to cook off the raw flour taste and create a roux.

Gradually pour in chicken broth while stirring constantly to prevent lumps. Add potatoes and thyme. Bring to a boil, then reduce heat and simmer for 10-12 minutes until potatoes are tender.

Stir in the cooked chicken, heavy cream, and frozen peas. Cook for 3-4 minutes until heated through and peas are tender.

Season with salt and pepper to taste. Serve hot, optionally garnished with fresh parsley or served with biscuits or puff pastry on top.