• Heat 3 tablespoons oil in a stock pot. Pat chicken dry and sprinkle with salt. Brown chicken in 4 batches, turning, about 5 minutes per batch, transferring as browned to a large bowl.
• Add enough of remaining oil to pot to total 1/4 cup fat, then stir in flour with a flat metal or wooden spatula and cook over moderately low heat, scraping back and forth constantly (not stirring), until roux is the color of milk chocolate, 10 to 20 minute
• Add enough of remaining oil to pot to total 1/4 cup fat, then stir in flour with a flat metal or wooden spatula and cook over moderately low heat, scraping back and forth constantly (not stirring), until roux is the color of milk chocolate, 10 to 20 minutes.
• Add onion, carrots, bell pepper, and celery and cook, scraping back and forth occasionally, until onion is softened, about 8 minutes.
• Add water to roux mixture and bring to a boil, stirring occasionally until roux is incorporated. (Roux will appear curdled initially, but will come together as it reaches a boil.).
• Add chicken and any juices accumulated in bowl, then simmer, partially covered, until chicken is cooked through, 30 to 35 minutes.
• Stir in cayenne, green onions, and salt to taste and serve over rice.

Tips

• Can be made 1 day ahead (green onions) and cooled completely, uncovered, then chilled, covered. Reheat, then stir in scallion greens.