Preheat the oven to 400°F / 205°C. Boil 1 small diced potato in water until tender, then drain.
Melt ⅓ cup of butter in a large saucepan. Cook ½ diced medium onion, 2 minced garlic cloves, ½ teaspoon of poultry seasoning, and ¼ teaspoon of dried thyme until the onion softens.
Add 1 large diced carrot, 2 diced celery ribs, and ½ cup of corn. Stir in ⅓ cup of all-purpose flour, then 1¼ cups of chicken broth and ⅔ cup of half-and-half, and cook until thickened.
Stir in the potato, 2½ cups of diced cooked chicken, ½ cup of frozen peas, and 1 tablespoon of chopped parsley.
Line a 9in / 23cm deep-dish pie pan with one of 2 pie crusts. Add the filling, cover with the second crust, seal the edges, and cut a few slits in the top.
Brush with 1 egg yolk beaten with a little water. Bake for 35-40 minutes, until golden, then rest for 10-15 minutes before cutting.
