Bring the stock to a simmer in a medium saucepan. Add the thyme leaves, then poach the chicken breasts until just firm and cooked through, 10-12 minutes. With a pair of kitchen tongs, transfer the poached chicken to a plate and let cool.

Tip the boiling onions into the stock and simmer for 5 minutes. Add the mushrooms and continue simmering until both the onions and mushrooms are tender, 4-5 minutes longer. Using a slotted spoon, transfer the onions and mushrooms to a large bowl.

Increase the heat under the stock and boil until it has reduced to 1¼ cups. Meanwhile, cut the chicken into bite-size pieces and add to the onions and mushrooms. When the stock has reduced, pour it into a pitcher.

Return the pan to the heat. Melt the butter in the pan and stir in the flour. Keep stirring over medium heat for 3-4 minutes. Gradually pour in the hot stock, stirring until smooth. Simmer until thickened, 5-10 minutes, then stir in the cream and bring back to a simmer. Season to taste with salt and pepper. The sauce should be thick and creamy. Pour it over the chicken and vegetables and mix well. Let cool completely.

Preheat the oven to 400°F. Divide the pastry into two portions: two-thirds and one-third. Roll out the larger portion on a lightly floured surface to a circle large enough to line a pie dish or pan, or a casserole, that is 9-10 inches in diameter and 1½-2 inches deep. Line the dish and trim off the excess pastry. For a good-looking result, put a pie bird or pie funnel in the middle of the dish. Spread the filling evenly in the dish.

Roll out the remaining pastry to form a lid for the pie and cut a cross in the middle to fit around the pie bird. (If you're not using a pie bird, cut a small cross anyway, to serve as a steam vent.) Brush the pastry rim with the egg wash, then drape the pastry lid over the pie and press down around the rim to seal. Use a sharp knife to cut off any excess pastry around the rim, then crimp the edges. If you wish, decorate the pie with pastry leaves made with the trimmings. Brush the pie top and trimmings with the egg wash and sprinkle the top with coarse sea salt. Bake until the pastry is golden brown and the sauce is bubbling from the steam hole, about 35 minutes.