Preheat. Heat the oven to 425°F. If using a bottom crust, fit one pie crust into a 9-inch deep-dish pie plate.

Sauté the vegetables. Melt the butter in a large skillet or Dutch oven over medium heat. Add the onion, carrots, and celery and cook for 8 minutes, until softened but not browned.

Make the roux. Sprinkle the flour over the vegetables and stir constantly for 2 minutes, until it smells lightly toasted.

Build the gravy. Slowly pour in the chicken broth while stirring. Bring to a simmer and cook for 3 to 4 minutes, until the sauce thickens enough to coat a spoon.

Finish the filling. Stir in the heavy cream, cooked chicken, peas, thyme, salt, and pepper. Simmer for 2 minutes, then remove from the heat and taste for seasoning.

Assemble. Pour the hot filling into the pie plate (over the bottom crust if using one). Lay the top crust over the filling, trim and crimp the edges, and cut 3 or 4 slits for steam.

Bake. Bake for 30 to 35 minutes, until the crust is deep golden brown and the filling bubbles at the vents. Shield the edges with foil if they brown too fast.

Rest and serve. Let the pot pie cool for 10 minutes so the filling sets. Slice and serve warm.