In a small heavy skillet dry-roast juniper berries over moderately high heat, stirring, until fragrant and shiny and in an electric coffee/spice grinder grind to a powder with salt, pepper, and thyme. Rub pheasant evenly with spice powder. Marinate pheasant, covered and chilled, at least 1 day and up to 2.While pheasant is marinating, make stock. In a small bowl soak porcini in hot water 20 minutes, or until softened. Remove porcini, squeezing out excess liquid, and reserve liquid. Wash porcini under cold water to remove any grit and chop them. Preheat oven to 350° F. Pat thighs dry, keeping breasts covered and chilled, and season with salt and pepper. In a 12-inch heavy skillet heat oil over moderately high heat until hot but not smoking and brown thighs on all sides, skin sides down first, transferring with tongs to a large flameproof casserole (preferably shallow). Pour off all but about 2 tablespoons fat from skillet and in fat remaining in skillet cook shallots and garlic over moderate heat, stirring, until softened. Add porcini, shiitake, white mushrooms, and salt and pepper to taste and sauté over moderately high heat, stirring, until liquid mushrooms give off is evaporated. Slowly add all but about 1 tablespoon reserved porcini liquid, discarding last tablespoon (which contains sediment), and boil until liquid is evaporated. Add gin and wine and bring to a boil. Remove skillet from heat and ignite liquid carefully. When flames die out return skillet to heat and boil until liquid is evaporated. Add 2 cups stock and bring to a boil. Pour mushroom mixture over thighs in casserole and braise thighs, covered, in middle of oven 1 1/2 hours, or until tender. Transfer thighs with tongs to a bowl and cool. Add breasts to mushroom mixture in skillet and cook on top of stove at a bare simmer, uncovered, turning once, 8 minutes, or until just cooked through. Transfer breasts with tongs to bowl and cool. Pour cooking liquid through a large fine sieve into a large bowl, reserving mushrooms, and measure liquid. Add enough remaining pheasant stock to measure 4 cups liquid total. In a steamer set over boiling water steam vegetables separately, transferring all vegetables to a large bowl. Allow about 5 minutes cooking time for just-tender celery; 8 minutes for just-tender turnips, parsnips, and onions; and 10 minutes for just-tender carrots. Cut pheasant breasts into 1 1/2-inch chunks and cut thighs into chunks, discarding skin and bones. In a 3-quart oval gratin dish (about 15 by 10 1/2 by 2 1/2 inches) or other shallow baking dish toss together vegetables and pheasant chunks. In a large saucepan combine stock mixture and reserved mushrooms and bring to a boil. Stir cornstarch mixture and add to stock mixture, stirring. Simmer sauce 2 minutes and season with salt and pepper. Pour sauce over pheasant mixture. Filling may be made 2 days ahead and chilled, covered. Bring filling to room temperature before proceeding. On a lightly floured surface roll out 1 pastry sheet into a 14-inch square, keeping remaining pastry sheet chilled. Cut three 1/4-inch-wide pastry strips and braid together for pastry braid around rim of baking dish. Continue to cut and braid more strips from pastry to fit around rim of baking dish, transferring braids to a tray. From remaining rolled-out pastry cut out 2 long feathers for decoration, transferring to tray. Chill braids and feathers. Preheat oven to 375° F. On lightly floured surface roll out remaining pastry sheet into a rectangle at least 2 inches larger than baking dish and brush evenly with some egg wash. Drape pastry, egg-wash side down, over baking dish. Trim corners of overhang and press overhang along rim and side of baking dish to seal. Brush crust evenly with some egg wash. Arrange pastry feathers on crust and braids around rim, pressing gently to make them adhere. Brush decorations with some egg wash and if desired with a small sharp knife score pastry feathers decoratively. Bake pie in middle of oven 35 to 40 minutes, or until pastry is golden brown and puffed slightly. Pie may be baked 1 day ahead, cooled completely, and chilled, covered loosely. Reheat pie, uncovered, in a 375° F. oven 35 minutes, or until heated through (pastry will darken slightly).