Place chicken, onion, celery, garlic, bay leaves, and liquid to cover the chicken by 1 inch in a large soup pot or small stockpot. Add salt and pepper and bring to a gentle simmer. Cook, skimming any foam that rises to the surface, until chicken is fall-from-the-bone tender, 45 minutes to 1 hour. (Add water if necessary to keep chicken submerged in liquid.) Remove chicken to a heatproof bowl and set aside to cool. Strain broth through a fine-mesh sieve and set aside. When chicken is cool enough to handle, remove skin and bones; discard. Pull meat into bite-size pieces and place in a bowl; refrigerate until needed.
While stock is simmering, make roux: In a large, heavy-bottomed Dutch oven, heat oil over medium-high heat; whisk in flour. Cook, stirring constantly, reaching every portion of the bottom of the pot, until roux begins to take on some color. Reduce heat to medium or medium-low and continue cooking and stirring constantly until roux reaches the color of milk chocolate. (The timing here will vary depending on your cooktop as well as the pan you are using; the most important thing is to not let any portion of the roux scorch, and to stir constantly until you've reached the desired color.) Add the chopped onions, celery, and bell pepper and cook, stirring frequently, until vegetables have softened, 5 to 7 minutes. If stock has cooled by this time, add it to roux-vegetable mixture along with cayenne and bay leaves, and stir to combine. (If stock has not cooled by the time vegetables have softened, set aside to cool; you should always add a hot stock to a cool roux or vice versa.)
Once roux and stock are combined, bring to a gentle simmer. Continue to simmer until sauce is thickened and flavorful, about 2 hours, skimming any foam or excess oil that comes to the surface.
While simmering, saute sausage in a large skillet over medium-high heat until browned on all sides. Add sausage to gumbo. Taste gumbo and season lightly with salt. Simmer for 2 hours.
After simmering, add chicken, chopped scallions, and parsley to gumbo. Stir well and continue to simmer for 30 minutes longer. Adjust thickness if necessary, then season with salt and cayenne to taste. Serve gumbo ladled over hot white rice in large shallow bowls, with hot sauce and file at the table for guests to use to their liking.
Cook's Note: Gumbo thickness is a matter of personal preference. Some folks enjoy a very thick gravylike sauce, and others prefer theirs to be more on the brothy side. Either is correct; make it how you like it!