Make a bed of onions and potatoes on the bottom of a roasting pan, just large enough to hold the ingredients. If the pan is too large, the juices will dry and the flavor will not be intense. Rub the inside of the chicken with ginger and half of the garlic. Rub the outside of the chicken with paprika. Place the chicken, breast up, on the bed of vegetables; sprinkle with the remaining garlic and herbs. Tuck fresh rosemary under the wings and legs of the chicken and under the edges of the vegetables.
Roast at 375°F. for about 1.5 to 2.0 hours, just until the leg begins to move freely. Past this point the breasts will be too dry. Carve the chicken into breast slices, legs, and thigh joints. Surround the chicken with the potatoes and onions, and pour the defatted pan juices over the entire dish.
Remove the skin and bones from the chicken, and cut the chicken meat into small bite-sized pieces. Remove the juices, onions, potatoes, and any fat remaining in the roasting pan, putting the fat into a small saucepan, and cutting the onions and potatoes into bite-sized pieces. Slice enough additional onions so that you will end up with 3/4 cup of onions. Warm the chicken fat over medium high heat, and cook the raw onion until brown. Remove the onion to add to the roasted onions and potatoes. Either soak the dried mushrooms to reconstitute or clean the fresh mushrooms. Remove any tough stems, cut into bite-sized pieces, and sauté briefly in the oil. Remove to a plate. Put the carrots and peas in a microwave proof bowl, and cook in the microwave on high for 2-3 minutes until just tender. Heat the oil again, add the 3 T. flour, and stir with a whisk for 1 minute. Slowly add the warm chicken broth, and continue to cook and stir until just thickened. Add the spices, and taste for seasoning. Put all the chicken and vegetables together in a bowl and add the thickened gravy. Stir to mix, and taste to correct the seasonings.
Put the flour, salt, and baking powder into a large bowl or the work bowl of a food processor fitted with the steel blade. Either cut in the shortening by hand, or pulse to cut in the food processor. Add the ice water and mix until a ball of dough is formed. Roll out the dough to a circle just larger than the top of your baking dish. Put the chicken mixture into the baking dish. Cover with the dough. Pinch the edges of the dough to stick to the top of the baking dish and form a nice edge. Cut a small steam hole in the top of the pastry. Bake at 375°F. for 30 minutes.