In a stock pot place the chicken, water to cover, salt, peppercorns, celery, onion, parsley and carrot. Bring to the boil and simmer 30 minutes. Remove the chicken and cook the water down to 3 cups. Strain and reserve the stock.
Preheat the oven to 200 degrees C.
Melt 5 tablespoons butter in a saucepan and add the flour, stirring. Add the reserved stock and keep stirring. When thickened and smooth, stir in the cream. Simmer 10 minutes.
Cut the broccoli into florets. Boil them in salted water about 2 minutes and drain.
Pull the chicken meat from the bones, discarding the skin. Shred the chicken into bite sized pieces.
Melt 2 tablespoons butter in a frypan and add the broccoli, sprinkling with salt, pepper and nutmeg. Cook 1 minute then add the chicken. Add two cups of the cream sauce and stir.
Add the egg yolk to the remaining sauce and reheat, stirring. Remove from heat.
Cook the pasta in boiling water until al dente then toss with remaining 1 tablespoon butter and salt and pepper to taste.
Place the pasta in a buttered baking dish. Spoon the chicken and broccoli on top. Spoon the remaining sauce over and top with the grated Parmesan. Bake 15 minutes.