Heat the oil in a large soup pot over medium heat.
Pat the chicken dry and season with salt and pepper.
Add the drumsticks to the pot and cook without moving for 5–6 minutes per side until browned all over. Depending on the width of your pot, you may need to cook the drumsticks in batches. Once you finish browning all the drumsticks, return them all to the pot.
Simmer the soup:
Add the onion, carrots, and celery to the pot around the drumsticks. Place the bundle of thyme on top. Pour in the broth and 2 cups of water and bring to a boil. Reduce heat and simmer uncovered for 30–45 minutes or until the chicken reaches 165ºF. Taste and add salt and pepper if needed. See note.
Cook the noodles:
Bring a medium pot of water to a boil. Once boiling, add the egg noodles and cook according to package directions. Drain, rinse, and set aside.
Finish the soup:
Remove the chicken drumsticks from the broth and transfer them to a plate. Add the cooked egg noodles, dill, and lemon juice to the broth and simmer for 2–3 minutes. Turn off the heat. Taste and season once more to your preferences.
To serve:
Transfer the soup to a large serving bowl or tureen. Arrange the drumsticks on top. Enjoy!
Notes
The longer you simmer, the better it will be! If you rapidly simmer the broth just slightly above low heat, the liquid should reduce by almost half. For a soup with more broth, simmer on the lowest heat so you don’t cook off so much of the liquid.