Prep your ingredients. Dice the onion, celery, carrots, and potatoes. Mince the garlic.
Shred or chop the cooked chicken. Keep peas and corn in the freezer for now.
Sauté the aromatics. Warm 1–2 tablespoons oil in a large pot over medium heat. Add onion, celery, and carrots with a pinch of salt.
Cook 5–7 minutes until softened and fragrant. Stir in garlic for 30 seconds.
Add potatoes and herbs. Toss in diced potatoes, thyme, and bay leaf. Stir for a minute to coat everything in flavor.
Pour in broth and simmer. Add 6 cups chicken broth.
Bring to a gentle boil, then reduce to a simmer. Cook 12–15 minutes, until potatoes are tender.
Thicken the soup. In a small bowl, whisk 3 tablespoons flour with 1 cup milk until smooth. For gluten-free, whisk 2 tablespoons cornstarch or arrowroot with 2 tablespoons cold water, then stir in milk.
Slowly pour into the pot while stirring. Simmer 3–5 minutes to thicken slightly.
Add chicken and frozen veggies. Stir in chicken, peas, and corn. Simmer another 3–4 minutes until hot.
If using Greek yogurt, remove the pot from heat and whisk it in to avoid curdling.
Season and finish. Taste and adjust with salt and pepper. Remove bay leaf. Stir in chopped parsley.
Add a splash more milk or broth if you prefer a looser texture.
Serve warm. Ladle into bowls. Garnish with extra parsley, cracked pepper, and a squeeze of lemon if you like a brighter finish.