Let’s dive into the creation of these pies, step by step:

1. Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
2. In a mixing bowl, combine the flour and salt. Add the diced butter, and using your fingertips, rub the butter into the flour until the mixture resembles coarse crumbs.
3. Add the ice-cold water gradually, mixing until the dough just comes together. Form into a ball, wrap in plastic, and refrigerate for 30 minutes.
4. While the dough chills, prepare the filling by mixing the shredded chicken, peas, carrots, cheddar cheese, and thyme in a bowl. Season with salt and pepper.
5. Once the dough is chilled, roll it out on a floured surface to about 1/8-inch thickness. Cut into circles using a cookie cutter or the rim of a glass.
6. Spoon the filling onto one half of each dough circle. Fold the dough over the filling to create a half-moon shape and press the edges with a fork to seal.
7. Brush the tops with the beaten egg for a golden finish.
8. Bake in the preheated oven for 25-30 minutes, or until golden brown.

Don’t rush the dough-making process; it’s in these moments of patience and care that the magic of a perfect pie pastry is born. I remember Mama Lou’s gentle touch as she worked the dough, a skill I strive to emulate each time.