Sauté Vegetables: In a large pot, melt butter over medium heat. Add onion, carrots, celery, and garlic. Sauté for 5–6 minutes until softened.
Make Roux: Sprinkle flour over the vegetables and stir for 1–2 minutes to cook off the raw flour taste.
Add Liquids: Gradually whisk in chicken broth and milk until smooth. Bring to a gentle simmer.
Simmer: Add diced potatoes (if using), thyme, salt, and pepper. Cook for 10–12 minutes until potatoes are tender.
Add Chicken & Peas: Stir in shredded chicken and frozen peas. Simmer for 5 more minutes until heated through. Adjust seasoning if needed.
Optional Garnish: Serve topped with crumbled pie crust or flaky biscuits for a true "pot pie" experience.