Preheat the oven to 400°F. Line a sheet pan with aluminum foil.
Place the chicken legs on the prepared sheet pan, drizzle with the olive oil, and season with 2 heavy pinches each of salt and pepper. Roast for 20 minutes, until lightly golden.
Meanwhile, in a large pot or dutch oven, combine the chicken stock and water and bring to a light simmer. Once roasted, add the chicken legs to the pot and simmer until cooked through and tender, 20 minutes more.
Transfer the chicken to a clean sheet pan to cool slightly. When the chicken is cool enough to handle, use two forks to shred the meat and discard the skin and bones. Set the meat aside.
While the chicken cools, add the carrots, celery, and parsnips to the pot and simmer until tender, 10 to 12 minutes. Remove from the heat.
Once shredded, stir the chicken into the soup along with the dill and parsley. Taste and adjust the seasoning with salt and pepper, then serve.