Place turkey carcass in large stock pot. (Fine if it's on end or sticking up out of the pot.)
Cover carcass with water.
Bring to a full boil, uncovered.
Reduce heat to low, cover pot, and simmer for 8-12 hours.
Add more water to keep carcass covered if needed.
Remove pot from heat and cool.
Chill/refrigerate soup until fat rises to the top and congeals.
Remove fat layer from the top of soup by skimming it off with a spoon and discarding.
Warm soup slightly over low heat on the stovetop.
Remove bones and skin from the soup and discard. See post above for tips to simplify this process.
Be very careful to remove all the tiny bones, as they are a potential choking hazard.
Once you think you've removed every bone, pour turkey broth through a woven metal strainer.
(For best results, see my tips above about the process.)
Heat soup on stovetop on medium high, stirring often.
Meanwhile, in a frying pan on the stovetop, sauté chopped celery, carrots and onions in a few tablespoons of olive oil over medium heat, until vegetables are just softening and onions are translucent.
Add sautéed vegetables to the soup and heat thoroughly.
Add cooked rice.
Add lemon juice and white wine.
Season with salt and pepper.
(I start with a teaspoon of salt and a 1/2 teaspoon of freshly ground pepper and taste test, then adjust if needed.)
A few minutes before serving, add frozen sweet peas.
Enjoy steaming hot with a slice of crusty fresh bread!