Preheat the oven to 425°F (220°C) and line a rimmed sheet pan. Place chicken thighs skin-side up, coat with 1 tablespoon oil, ½ teaspoon salt, ½ teaspoon pepper, and ½ teaspoon thyme. Roast for 25–35 minutes, until the thickest part reaches 165°F (74°C). Rest for 10 minutes.
While the chicken roasts, heat the remaining tablespoon of oil in a large pot over medium heat. Cook onion, carrots, celery, and ½ teaspoon salt for 8–10 minutes, until the onion is translucent and carrot edges begin to soften.
Stir in garlic, remaining thyme, and ¼ teaspoon pepper for 30 seconds. Add broth, water, and bay leaves. Bring to a gentle boil, reduce to a steady simmer, and cook for 12 minutes.
Spoon the clear roasting juices from the sheet pan into the pot, leaving thick fat and scorched spots behind. Remove and discard chicken skin and bones, then pull the meat into spoon-sized pieces.
Remove bay leaves. If saving portions for later, transfer the desired amount of soup base to containers now, before adding noodles. Bring the remaining soup to a lively simmer, add noodles, and cook for 1 minute less than the package's lower time estimate, stirring twice.
Return shredded chicken and any cutting-board juices to the pot. Simmer for 2 minutes, then turn off the heat. Fold in dill and parsley, rest for 5 minutes, and adjust salt and pepper to taste.