Place the turkey carcass in a large stock pot, and cover with water. Add the bay leaves, peppercorns, allspice, poultry seasoning, onion, carrots, and celery. Simmer, stirring occasionally, for 3-4 hours.
Strain broth through a fine mesh strainer or cheesecloth. Return strained broth to pot, and bring back up to a simmer. Add in chopped carrots, celery, and rice.
Noodles
Place flour in a large bowl. Make a well in the middle and add the eggs.
Beat the eggs in the center of the well, and then add salt and half and half. Mix well.
Slowly start incorporating the egg mixture into the flour mixture until a soft dough forms.
When the dough is able to be formed into a ball, remove from the bowl and coat with a thin layer of oil. Wrap in plastic wrap and refrigerate for 10-15 minutes, or until ready to use.
Roll out into a thin sheet and cup with a pizza cutter into small strips. Add to boiling soup, stirring as you add them, and cook until done, approximately 2-4 minutes.