Cut in the butter until the mixture resembles coarse crumbs.
Add the ice water, 1 tablespoon at a time, until a dough forms.
Divide the dough into 8 portions, flatten into discs, wrap and refrigerate 1 hour.
Heat the oil in a large skillet over medium-high heat.
Season the chicken with salt and pepper.
Transfer the chicken to the skillet and cook until browned (5-6 minutes). Remove and set aside.
Cool the chicken until it's safe to handle, then dice it into ½-inch cubes.
To the same pan, add the onion, carrots, and celery and cook until softened (5 minutes).
Add the garlic and thyme, cook 1 minute.
Sprinkle flour over the vegetables, stir 1 minute.
Gradually whisk in the stock and cream.
Simmer the sauce until thickened (3-4 minutes).
Return the chicken to the pan and add the peas.
Season to taste, and let cool completely.
Preheat the oven to 400 F.
Prep a baking sheet with parchment paper.
Flour your working surface, and roll each dough disc into a 7-inch circle. You can roll it between two pieces of cling wrap plastic or parchment paper to avoid sticking.
Place ¼ cup of filling on one half of the circle, leaving a ½-inch border.
Fold the other half over and seal the edges with a fork. Cut off any extra dough to give it a neat appearance (you may get an extra pie from the extras).