Preheat the oven to 400 degrees F. Grease a 9 by 9 by 2-inch square baking pan.
In a large saute pan, melt the butter. Add the onions and celery and saute for 2 minutes. Season with salt and pepper. Stir in the flour and cook for about 3 to 4 minutes for a blond roux. Stir in the chicken stock and bring the liquid up to a boil. Reduce to a simmer and continue to cook for 4 to 6 minutes, or until the sauce starts to thicken. Stir in the half and half and continue to cook for 4 minutes. Season with salt and pepper. Stir in the potatoes, carrots, peas and chicken. Mix the filling thoroughly. Line the baking pan with one of the crusts. Pour the filling into the prepared pan. Place the top crust on top of the filling. Carefully tuck the overlapping crust into the pan, forming a thick edge. Crimp the edges of the pan and place on a baking sheet. Place the sheet in the oven and bake for about 25 to 30 minutes or until the crust is golden brown and crispy.
Remove from the oven and cool for 5 minutes before serving.
Combine the flour and salt in a bowl. Add the lard and work it in with your hands until the mixture resembles coarse crumbs. Add the water, 1 tablespoon at a time, working it in with your hands. Add only as much as you need to make a smooth ball of dough. Wrap it in plastic wrap and refrigerate for at least 30 minutes. Remove the dough from the refrigerator and place it on a lightly floured surface. For 2 crusts, cut the dough in two and put the second half back in the refrigerator. For each crust, roll the dough out on the floured surface into a square about 14 inches in diameter and 1/8-inch thick. Gently fold the square of dough in half and then in half again so that you can lift it without tearing it, and unfold into a square baking pan. Fill and proceed as directed in the recipe.