Melt the butter in a large pot over medium heat, then toss in the diced onion, celery, and carrots. Sauté for roughly 5 minutes until the vegetables begin to soften. Stir in the minced garlic, bay leaves, and diced potatoes, then dust everything with flour, mixing well so the vegetables are evenly coated and the flour loses its raw texture.

Pour in the chicken broth along with the milk and fresh thyme, giving everything a good stir. Turn the heat down to low and let the mixture gently simmer for about 20 minutes, or until the potatoes turn fork-tender.

Fold in the shredded chicken, peas, and corn, then season generously with salt and pepper. Allow the soup to keep simmering for another 10 minutes so the flavors meld — if it feels too thick, splash in a bit more milk to loosen it up.

Discard the bay leaves and mix in the fresh parsley just before serving. Spoon the hot soup into bowls and top with pie crust crackers, if you're making them.

For the pie crust crackers, preheat your oven to 375°F. Roll out a pie crust (store-bought works fine) and lay it flat on a baking sheet lined with parchment or a Silpat mat. Lightly brush with melted butter and sprinkle with salt, then slice into thick strips using a pizza cutter. Bake for 12–15 minutes until golden and crisp, then let cool before breaking into pieces to serve alongside the soup.