2. Remove the chicken from the broth with tongs and set aside. When the chicken is cool enough to handle, cut it into small pieces and place it in a large casserole baking dish.
3. Meanwhile, add the mushrooms, carrots, turnips and potatoes to the broth and simmer until they are just tender, about 10 minutes. Transfer them to the baking dish with a slotted spoon.
4. Strain the broth and reserve it in a bowl. Heat the olive oilin the now empty saucepan over medium heat. Add the onions and thyme and cook until the onions soften, about 5 minutes.
5. Whisk in 1/4 cup of the flour and stir for 3 or 4 minutes. Whisk in the reserved broth, slowly at first and then more quickly. Bring the sauce mixture to a boil and cook until the mixture thickens enough to coat a spoon. Pour the sauce into the baking dish and season well with salt and pepper.
6. Preheat the oven to 400ºF.
7. To make the crust, mix the cornmeal, remaining cup of flour, sugar, baking soda and salt together in a food processor. Add the butter and process until the butter is the size of small peas. With the food processor running, slowly add the buttermilk until the mixture forms a dough. Remove the dough from processor, form it into a ball and roll it out on a floured surface until the dough is 1/4-inch thick.
8. Place the dough on top of the baking dish and trim it so that it fits inside the dish. Cut a few slits in the dough to allow the steam to escape. Place the pie in the oven and bake until the crust is golden brown and the sauce is bubbling, about 30 minutes. Let the pot pie stand for 10 minutes before serving.