COOK BIRDS: Split pheasant down the breastbone (or have your butcher do this).
Rinse the halves, place in a deep pot and barely cover with water.
Add bay leaf, onion, carrot, celery, salt and peppercorns.
Bring to rolling boil, then turn down heat and simmer for approximately 30 minutes, or until tender.
Remove foam and scum as it forms.
Remove bird(s) from broth, reserving the broth.
Using a heavy skillet, sauté the halves in about 2 tablespoon of the butter until golden.
Place birds into small roasting pan or casserole with just enough water to cover the bottom of the pan.
Sprinkle with thyme and rosemary.
Bake, lightly covered with foil, for 30 to 40 minutes at 350℉ (180℃).
MAKE GRAVY: While the birds are in the oven, strain the broth Brown the mushrooms using the same skillet in which you browned the pheasant. Remove the mushrooms and keep them warm. Melt the remaining 2 tablespoon of butter in the skillet. Add the flour, stirring up the browning from the pan. Cook over moderately high heat until golden brown. Blend in the broth using a wire whisk. Add mushrooms and continue cooking approximately 1 to 2 minutes. Turn down heat, cover and keep warm until pheasant is roasted. When the pheasants are cooked, remove them from the oven and scrape the herbs from the skin. After placing the pheasant halves on a warm platter (or leaving them in the casserole), pour the gravy over the pheasant. Garnish with the chopped nutmeats and serve. This dish is particularly good with wild rice. You can substitute rock Cornish hen, guinea fowl, or chicken for the pheasant and hazelnuts, filberts or walnuts for the black walnuts.