In a mixing bowl, combine all-purpose flour and salt with shortening until the mixture resembles coarse crumbs. Gradually add milk, mixing until a soft dough forms. Wrap it in plastic wrap and refrigerate for 30 minutes to chill.

While the dough chills, preheat your oven to 425°F (220°C). Once ready, roll out the chilled dough to about 1/8-inch thickness and cut it into desired shapes.

Bake the pastry shapes in the preheated oven for 8-11 minutes until golden brown.

In a large Dutch oven, melt butter over medium-high heat. Add diced potatoes, chopped onion, celery, and sliced carrots. Sauté for about 5-7 minutes until softened.

Sprinkle flour over the sautéed vegetables and stir until coated. Gradually whisk in the chicken broth, ensuring no lumps form, and bring to a gentle boil. Simmer for 8-10 minutes until thickened.

Stir in your cooked chicken and frozen peas and corn. Cook for an additional 3-5 minutes until heated through.

Ladle the soup into bowls, topping each with the freshly baked pastry shapes.