Preheat and prep. Heat the oven to 400°F (200°C).
If using refrigerated pie crust, let it sit at room temperature for about 10 minutes so it’s easier to handle.
Sauté the vegetables. In a large skillet or pot, warm the olive oil or butter over medium heat. Add onion, carrots, and celery. Cook, stirring, until softened, about 6–8 minutes.
Add the garlic and cook 30 seconds, just until fragrant.
Make the roux. Add the 4 tablespoons butter to the pan. Once melted, sprinkle in the flour. Stir constantly for 1–2 minutes to form a smooth paste.
This cooks off the raw flour taste and thickens the sauce later.
Build the sauce. Slowly pour in the chicken broth while whisking to avoid lumps. Add the milk or half-and-half and keep whisking. Simmer 3–5 minutes until thick and creamy.
If it gets too thick, add a splash more broth.
Season and add mix-ins. Stir in salt, pepper, thyme, parsley, and poultry seasoning. Taste and adjust seasoning. Fold in the chicken, peas, and corn.
Remove from heat and let it cool slightly while you prep the crust.
Line the pie dish. Fit one pie crust into a 9-inch pie dish, pressing it into the corners. Trim any long overhang, leaving about 1/2 inch around the rim.
Fill the pie. Spoon the warm filling into the crust and spread it evenly. Don’t overfill; keep it just below the rim.
Top and seal. Place the second crust over the filling.
Trim excess, then fold and crimp the edges to seal. Cut 4–5 small slits on top for steam to escape. Brush with the egg wash for a glossy, golden finish.
Bake. Set the pie on a baking sheet to catch drips.
Bake for 35–45 minutes, until the crust is deep golden and the filling is bubbling through the slits.
Rest before serving. Let the pot pie sit for at least 15 minutes before slicing. This helps the filling set so it doesn’t spill out.