Sauté the aromatics. In a large skillet or pot, melt the butter over medium heat. Add onion, celery, and carrots. Cook until softened, about 6–8 minutes. Stir in garlic and thyme for the last minute.

Build the roux. Sprinkle flour over the vegetables and stir for 1–2 minutes. The mixture will look thick and slightly pasty. This step removes the raw flour taste and helps the sauce thicken later.

Add the liquids. Slowly whisk in chicken broth, then milk or half-and-half. Keep stirring until the sauce is smooth and begins to simmer. Cook 3–4 minutes, until it thickly coats a spoon.

Stir in chicken and peas. Add the cooked chicken and peas. Season well with salt and black pepper. Taste and adjust—this is your moment to get the seasoning right.

Cool the filling. Take the pan off the heat and let the filling cool to room temperature. Do not add hot filling to a crust or you risk a soggy bottom and steam-related cracks when freezing.

Assemble the pie. Line a 9-inch pie dish with the bottom crust. Spoon in the cooled filling. Top with the second crust. Trim, crimp the edges, and cut a few slits for steam.

Add egg wash. Brush the top with the egg wash for color. If freezing, you can also wait to brush just before baking; both options work.

To bake now: Preheat oven to 400°F (200°C). Place pie on a sheet pan. Bake 35–45 minutes until golden and bubbly. Let rest 10–15 minutes before slicing so the filling can set.

To freeze unbaked: Wrap the assembled pie tightly with plastic wrap, then foil. Label with date and baking instructions. Freeze for up to 3 months.

Bake from frozen: Remove plastic, keep foil loosely tented for the first 30 minutes. Bake at 400°F (200°C) for 60–75 minutes total, removing foil when the top is pale golden so it can brown. If the edges brown too fast, shield with foil. Rest 15 minutes before serving.