Collect all the leftover turkey bones and meat, omitting the skin. Put them into a big enough stockpot that you can add at least two gallons of water. Add the bay leaves, cut-up onion, celery, thyme, and peppercorns. Bring to a light boil, then reduce heat to lowest setting. Simmer for and hour or two
Strain the stock. Set the bones and the meat aside; discard the vegetables. If you like, you can put the process on hold at this point by letting the stock cool and refrigerating it, along with the turkey bones and meat
To complete the gumbo, blend the flour and the oil in a saucepan and make as dark a roux as you can, stirring constantly to avoid burning it. (The higher the heat, the more assiduously you must stir.)
When the roux is medium-dark, turn down the heat and add the onion, bell pepper, celery and parsley. Sauté them in the roux until the onions are clear and have begun to brown a little.
Skim the fat off the top of the stock, and add it to the roux. Bring to a light boil.
While that's happening, pick the meat from the turkey bones and set aside. Slice the andouille into one-inch-thick discs. Wrap them in paper towels and microwave them on medium power for about three minutes, to remove excess fat. Add the turkey meat and the sausage to the gumbo pot.
Lower to a simmer and cook the gumbo for one to two hours. Stir every now and then.
Serve over cooked long-grain rice. Scatter some green onions over the top, and a pinch or two of filé at the table.