4 tablespoons (1/2 stick) butter
1 medium onion, finely diced
2 medium carrots, finely diced
1 stalk celery, finely diced
1/4 cup all purpose flour
3 cups low-sodium chicken broth, plus more as needed
1/4 cup dry white wine (or chicken broth)
2 cups shredded or chopped cooked chicken breast
1/4 teaspoon ground turmeric
1/2 teaspoon ground thyme
Kosher salt and freshly ground pepper
1/4 cup half-and-half
2 rounds refrigerated pie crust
1 large egg
4 6-inch individual foil pie pans or a standard muffin tin
1. Melt the butter in a large skillet over medium-high heat, then add the onion, carrots and celery. Cook, stirring the vegetables around, until they start to soften, about 3 minutes. Sprinkle the flour over the veggies and stir to combine. Cook the flour-coated veggies for 1 minute, then pour in the chicken broth (and wine, if using!) and stir to combine. Let it heat up and start to bubble and thicken, about 3 minutes.
2. Stir in the chicken, then add the turmeric and thyme, then season with salt and pepper. Add the half-and-half, then stir the mixture and let it bubble up and thicken, about 3 minutes. If it seems overly thick, splash in a little more broth. Turn off the heat and let the filling cool to room temperature.
3. Meanwhile, roll out the pie crusts slightly and cut out 8 dough circles just a bit larger than the pie pans (if using a muffin tin, you'll need sixteen 3 3/4-inch circles). Press a dough circle into each pie pan (or 8 muffin cups), making sure the dough comes almost to the top of each pan. Fill the pies with the chicken mixture. Lay a second round of dough over the top of each pie. Press the dough so that the edges meet, then use a fork to seal the edges. Mix the egg with 2 teaspoons water and brush it all over the surface of the crust. (Discard any extra egg wash.) Cut small vents in the surface of the crusts.
4. If you're baking the pies right away, preheat the oven to 350 degrees F, place the pies on a baking sheet and bake 25 to 30 minutes, until the crust is deep golden brown and the filling is bubbly. Serve them straight out of the pie pans or turn them out of the pan and serve them upside down!
Cook's Note: FREEZE IT! Place the pies on a baking sheet and flash-freeze 45 minutes. Then cover tightly with heavy-duty foil and freeze up to 6 months. To bake, preheat the oven to 350 degrees F. Bake the foil-covered pies for 1 hour (or 35 minutes for muffin-size pies). Remove the foil and bake 30 to 50 minutes more (10 to 15 minutes for muffin size), until hot and bubbly.