These mini chicken pot pies are irresistible.
Swap idea: Instead of making a crust, use store-bought biscuit dough.
For the filling:
Place 1 tablespoon vegetable oil into a 10-inch cast-iron skillet and set over high heat until it shimmers. Add the chicken, season with 1 teaspoon of salt, and cook, stirring occasionally, until the chicken is no longer pink on the outside but not dry, 4 to 6 minutes. Remove the chicken from the skillet and set aside in a medium bowl.
Decrease the heat to medium and heat the remaining tablespoon vegetable oil in the skillet until it shimmers. Add the onions, mushrooms, carrots, celery, garlic, remaining 1½ teaspoons of salt, black pepper, dried thyme, and dried tarragon, and stir to combine. Cook, stirring occasionally, until the onions have softened, about 5 minutes. Add the butter and melt. Stir in the flour and cook for 1 to 2 minutes. Gradually stir in the chicken broth and milk. Bring to a simmer, stirring continually. Continue stirring until the sauce thickens, about 3 minutes. Remove the skillet from the heat and stir in the peas, thyme, tarragon, and reserved chicken. Cover and set aside.
For the crust:
Sift the flour into a bowl. Add in the salt and cubed butter. Fold the ingredients together so that the flour has evenly coated each cube and they are not sticking together. Using your fingers crush the butter into the flour to make a uniform texture about the size of a pea. Pour in ¾ of the water and fold the dough together until a rough ball is formed. Add the remaining water as needed. Without overworking the dough, continue working the dough until it is mostly smooth and all incorporated. Turn the dough out onto a floured cutting board. Cut the dough into quarters, wrap with plastic wrap and refrigerate for at least 1 hour or overnight so the dough can relax.
Position an oven rack in the middle of the oven and preheat to 425ºF.
Remove the pie crust from the refrigerator and roll out the dough to create 4 rounds about 1/6-inch thick. Ladle the warm chicken pie filling in 4 ramekins and place them on a parchment lined cookie sheet. Place the pie dough on top of each ramekin and attractively flute the edges. You can cut away the excess pie dough and crimp with a fork if you like.
With a fork whisk the egg and water together to make the egg wash. Brush the top of the 4 pies with the egg wash.
Place the pies into the oven and bake on the center rack for 15 minutes until the crust is fragrant and golden brown. Remove the pies from the oven, let rest for 10 minutes and then serve at once. Enjoy.