Roast the Chicken& Vegetables: Preheat oven to 375°. Rub chicken with 1 T olive oil& sprinkle generously, inside& out, with salt& pepper. Toss potatoes, carrots, onions, garlic, mushrooms,& herbs with remaining 2 T olive oil& some salt& pepper. Set the chicken breast-side down in a large flameproof roasting pan& scatter the vegetables around the chicken. Roast for 1 1/4 hours, stirring vegetables several times. Remove chicken form the pan to cool. Remove vegetables with a slotted spoon& set aside in a bowl with the peas. Don't clean out the roasting pan. When the chicken has cooled (at least 15 minutes) pull the meat form the bones, discarding skin& bones. Cut meat into small chunks (1/2" to 1") & set aside (do this after the sauce is made or while someone else is making the sauce). Make the Sauce: If there are not a lot of juices & fat in the pan, skip to step 15. If there are, pour the fat & juices into a measuring cup or gravy separator; separate the fat from the juice. Add juices to the chicken stock& add enough butter to the fat to make 6 T total fat & butter. Put the roasting pan (which should still have caramelized bits in it from the chicken& vegetables) on the stove over medium heat. Pour in the 6 T fat+butter; when melted & bubbling, add flour & stir constantly to make a smooth roux. Scrape up any caramelized bits. Cook the roux, stirring constantly, until lightly browned, about 5 minutes. Add the stock, bring to a boil,& simmer. Continue to stir & scrape the bottom of the pan. Cook the sauce for at least 15 minutes, whisking occasionally, until it is as thick as heavy cream. Season with salt, pepper,& more herbs to taste. Make the Egg Wash: Whisk together the egg yolk& cream. Set aside. Assemble the Pot Pie (s): Preheat oven to 400°. Choose 4 ovenproof bowls (18 oz each) OR a 2-qt casserole. Cut out a circle template of foil or paper that is about the size of the rim of each bowl or casserole. Divide the chicken, vegetables,& sauce among the dishes. Place on a baking sheet (to catch any drips in the oven). For individual pies: On a floured board, cut the dough into 4 pieces. Quickly roll out each piece into a larger circle than the circle template (the extra dough will drape down the sides of the bowls). Remember to work quickly so the butter in the pastry doesn't start to melt- you may need to sprinkle dough to keep the pastry from sticking. As each one is rolled out, place on top of the filled bowls, pressing along the edges. For one large pie, lay the dough on a floured board& roll out to a the same shape, but larger than, the casserole template (the extra dough will drape down the side). Remember to work fast so the butter in the pastry doesn't start to melt- you may need to sprinkle dough to keep the pastry from sticking. Lay the dough on top of the filled casserole& press along the edges. Brush the Egg Wash onto the pastry with a pastry brush. You do not need to make any vent holes- steam will escape along the edges of the pastry. Bake for 30 to 55 minutes, until the crust is thoroughly browned& puffed. NOTES: Advance Preparation: The Puff Pastry and the filling (chicken, vegetables,& sauce mixed together) can be made 1 to 2 days ahead of time& refrigerated. The Puff can even be frozen for a few weeks.