In a large bowl, combine all-purpose flour and salt. Cut in shortening using a pastry cutter until the mixture resembles coarse crumbs. Gradually add milk, mixing until a soft dough forms. Shape the dough into a disk, wrap it in plastic, and refrigerate for 30 minutes or overnight.

Preheat your oven to 425°F (220°C). Roll out the chilled dough to about 1/8-inch thickness, cut out shapes, and arrange them on a baking sheet lined with parchment paper. Bake for 8-11 minutes until golden brown, then set aside.

In a Dutch oven over medium heat, melt 2 tablespoons of butter. Add diced potatoes, chopped onion, celery, and sliced carrots. Sauté for about 5-7 minutes until onions are translucent and aromatic.

Sprinkle in the all-purpose flour, salt, and pepper over the sautéed vegetables. Stir, allowing the flour to absorb the butter. Gradually whisk in chicken broth, bring to a boil, reduce heat, and simmer for 8-10 minutes until potatoes are tender.

Stir in shredded chicken, frozen peas, and corn. Cook for an additional 5 minutes until everything is heated through and vibrant.

Ladle soup into bowls, topping each with baked pie crust shapes for that homestyle touch.