Sometimes you just need a chicken pot pie. I learned to love savory pies during my years in England. Cornish pasties, raised game pies with a hot-water crust, steak and kidney pudding with a suet crust - these are rich, substantial meals designed to satisfy a big hunger in a cold climate. This pie is silky and rich, but I've streamlined it by substituting milk for cream in the velouté sauce and sautéing the onions and mushrooms in vegetable oil instead of butter. But it's still plenty and satisfying!

To make the cornmeal crust:
In a food processor fitted with the metal blade, combine the flour, cornmeal, baking powder, and salt and process just to mix. Add the butter and process in short bursts, scraping down the sides of the bowl as necessary, until the mixture resembles coarse bread crumbs. Add the whole egg, egg yolk, lemon zest, and 1 tablespoon ice water and process again for a few short bursts, scraping down the sides, until the dough just comes together, but is still a bit crumbly. If the dough seems very dry, sprinkle up to 1 more tablespoon of water over the mixture. Do not over-process or the crust will be tough. Turn the dough out onto a lightly floured surface and work together into a ball the consistency of stiff Play-Doh, press down into a round disk, and wrap with plastic. Refrigerate the dough for at least 1 hour or overnight.

To make the filling:
In a medium saucepan, bring the chicken stock to a simmer, add the carrots and thyme, and simmer for 4 minutes. Strain the stock into a heatproof jug and set aside. Remove and discard the thyme. Set the carrots aside.

In a medium skillet, heat the vegetable oil over medium heat and sauté the onion and the mushrooms, stirring occasionally, for about 10 minutes, or until they are tender and most of the liquid has evaporated. Add salt and pepper to taste, remove from the heat and set aside.

Dry the saucepan you used to cook the carrots. Add the butter and heat it over medium heat. Remove from the heat and stir in the flour to make a thick paste. Return the pan to the heat and stir the flour roux until it is bubbling but not brown, about 3 to 4 minutes. Gradually add the reserved chicken stock all at once, stirring until the mixture is smooth. Add the milk and simmer the sauce for 15 minutes, or until it is thickened, stirring occasionally to keep the sauce at the bottom of the pan from scorching. Remove from the heat and stir in the carrots, mushrooms, pearl onions, parsley, chicken, and lemon juice. Taste and adjust the seasoning.

Preheat the oven to 375°F. Butter the bottom and sides but not the top edge of a round or oval ceramic baking dish, about 1 1/2-quart capacity, and set it aside.

Quickly roll out the dough between 2 large sheets of plastic wrap to a size that will fit over your baking dish. The crust will have a rough and rustic appearance. Refrigerate the rolled dough for 20 minutes more, or until it is firm again.

Turn the chicken filling into the baking dish and brush the top edge of the dish with some of the milk. Place the rolled dough on a work surface next to the baking dish and peel away the top sheet of plastic wrap. Gently invert the dough over the baking dish, using the plastic to transfer it, then peel away the remaining plastic. Gently press the edges to secure them to the dish. With a sharp knife, cut 2 steam vents in the top, then brush the top of the dough lightly with milk.

Bake the pie for 20 minutes, then reduce the heat to 300°F. Continue to bake for 10 to 15 minutes more, or until the crust is shiny and golden. Allow to stand for 10 minutes before serving.

NOTES: Polenta may be substituted for the medium-grind cornmeal for a really toothsome crust. Add 1 or 2 extra tablespoons of water when making up the dough.