Pat the chicken dry with paper towels and season with salt and pepper. In a large dutch oven over medium heat, toast the 6 tablespoons of flour, stirring constantly, until just beginning to brown, about 5 minutes. Transfer flour to a medium bowl and wipe out pot. Heat 1 tablespoon of oil in now empty Dutch oven over medium-high heat. Add the chicken and cook until well browned on both sides, about 5 minutes per side; transfer to a plate. Pour the fat in the pan into another small bowl; set aside. There should be about 2 tablespoons of fat. If there is less fat than that left, add enough vegetable oil to equal 2 tablespoons. When chicken is cool enough to handle, remove and discard the skin.
Return the empty pot to the stove and heat over medium-high heat 1 tablespoon of vegetable oil. Add the onion, carrot, and celery and cook until softened, about 5 minutes. Stir in the thyme and cook until fragrant, about 30 seconds. Add 7 ½ cups of broth, chicken, and bay leaves and bring to a boil. Reduce the heat to low and simmer, covered, until the chicken is cooked through, about 20-25 minutes. Remove from the heat and transfer chicken to a clean plate. When chicken is cool enough to handle, shred into bite-size pieces, discarding bones.
Meanwhile, combine remaining ½ cup chicken broth, 2 tablespoons of the reserved chicken fat, and remaining tablespoon of oil in a liquid measuring cup. In the bowl of a food processor, process the remaining 2 cups of flour and ½ teaspoon of kosher salt. With the machine running, slowly pour in the broth mixture and process until it resembles a coarse meal. Turn dough onto a very lightly floured work surface and knead until smooth. Divide dough in half.
Following photos, roll each dough half into a 10-inch square. Cut each square into twenty 5-inch by 1-inch rectangles. Place several noodles on a parchment-lined baking sheet, cover with another sheet of parchment, and repeat stacking with remaining noodles, ending with a sheet of parchment. Freeze until firm, at least 10 minutes or up to 30 minutes.
Return broth to a simmer and add the noodles. Cook until the noodles are nearly tender, about 12-15 minutes, stirring occasionally to separate. Remove 1 cup of broth and whisk into the reserved toasted flour. Stir broth-flour mixture into pot being careful not to break up noodles. Simmer until lightly thickened, 3 to 5 minutes. Add shredded chicken and cook until heated through, about 1 minute. Season with salt and pepper and stir in parsley. Enjoy!