Reduce the heat to medium-low or a gentle simmer and add the white onion, carrot, bell pepper, celery root, parsley root and thyme. If necessary, add more water to the pot for a total of 5 quarts. Cover partially with a lid and cook, stirring occasionally, until the vegetables have slightly softened, around 15 minutes. Add the beans, tomato paste, reserved shredded turkey meat and bones, and cook, stirring occasionally, until the vegetables are soft and fork-tender, around 10 minutes. Add the garlic, tarragon, and half the parsley. Cook for 2 minutes, taste for seasoning and adjust with salt and pepper as desired.