Cut chicken into serving pieces. Place in a deep, heavy skillet, add the salted water and simmer until about half done (approximately 1¼ hours). Put chicken in a large buttered casserole. Blend together the next set of ingredients:
Cook over a very slow fire until the consistency of medium cream sauce. Pour over chicken.
Preparing the Rice - Put the rice in a heavy saucepan which can be covered. Add the milk and salt and let come to a boil. Turn the heat very low, cover and cook 30 minutes, or until grains are nearly dry. Lift the lid from the pans as little as possible, and if you must stir, do it once only, gently, with a fork, to keep the rice flaky.
Mix sugar, paprika, butter and nuts and add to the rice slowly.
When rice has cooled, mix with the beaten eggs, saving 1½ tablespoons of the beaten eggs for the crust.
Place the rice mixture as a mound over the chicken. Cut a gash in the crust of rice to allow the steam to escape. Bake in a preheated moderate oven (350°) until the chicken is tender (about 1 hour). Brush with the reserved beaten egg mixture. Spread the buttered crumbs over the surface. Sprinkle minced parsley over crust after removing casserole from oven.
If you want gravy, remove a small quantity of liquid from the casserole before the rice is placed over the chicken, because the rice will absorb most of the liquid.