Method
- Let the pie dough sit at room temperature for 10 minutes so it's pliable enough to work with without cracking. Preheat your oven to 400 F.
- Melt the butter in a large saucepan or Dutch oven over medium heat. Add the onion, carrots, and celery and cook, stirring occasionally, for 7 to 8 minutes until softened and the onion turns translucent.
- Add the garlic and cook for 30 seconds, stirring constantly, until fragrant but not browned.
- Sprinkle the flour evenly over the vegetables and stir constantly for 1 to 2 minutes, coating everything; this cooks off the raw flour taste and forms the base that will thicken the filling. It's normal for the mixture to look pasty and clump slightly at this stage.
- Slowly pour in the chicken broth while whisking constantly to smooth out any lumps, then add the milk and continue whisking until the mixture is smooth.
- Increase the heat to medium-high and bring the mixture to a gentle boil, stirring frequently, then reduce heat to medium-low and simmer for 4 to 5 minutes, stirring often, until it thickens to the consistency of a thin gravy that coats the back of a spoon.
- Stir in the cooked chicken, frozen peas, thyme, salt, and pepper. Cook for another 2 minutes just to heat through and let the peas thaw. Taste and adjust seasoning; the filling should taste well-seasoned since the crust adds no salt of its own.
- Remove the filling from the heat and let it cool for 10 minutes while you prepare the crust; hot filling can make the bottom crust soggy or start cooking the dough unevenly if poured in immediately.
- Fit one round of pie dough into a 9-inch pie dish, pressing it gently into the bottom and up the sides without stretching it (stretched dough shrinks back during baking).
- Pour the slightly cooled filling into the crust, spreading it into an even layer.
- Lay the second round of dough over the top, trim any excess overhang to about 1/2 inch, then fold the edges under and crimp with your fingers or a fork to seal. Cut 4 to 5 small slits in the top crust to let steam escape; skipping this can cause the top to bubble up or crack unevenly.
- Brush the top crust evenly with the beaten egg for a shiny, deep golden finish.
- Place the pie on a baking sheet (to catch any drips) and bake at 400 F for 35 to 40 minutes, until the crust is deep golden brown all over and you can see the filling bubbling gently through the steam slits.
- Remove from the oven and let the pie rest for 10 to 15 minutes before slicing; this allows the filling to set slightly so it doesn't run everywhere when you cut into it.
Tips
Let the filling cool slightly before pouring it into the crust, since piping-hot filling can start melting the butter in the dough before it even hits the oven.
Always cut steam vents in the top crust; without them, trapped steam can make the crust soggy or cause it to crack open unevenly.