In a large pot, heat the vegetable oil over medium heat. Add the chopped onion and cook until translucent, about 5 minutes.
Add the minced garlic and cook for another minute.
Add the chicken pieces to the pot and cook until they are browned on all sides.
Pour in the water and bring to a boil. Skim off any foam that forms on the surface.
Add the sliced carrots, bay leaves, thyme, dill, salt, and pepper to the pot.
Reduce the heat to low, cover, and let it simmer for about 45 minutes to 1 hour, or until the chicken is cooked through and tender.
Remove the chicken pieces from the pot and set aside. Discard the bay leaves.
Add the egg noodles or small pasta to the pot and cook according to the package instructions, usually about 5-7 minutes, until tender.
While the noodles are cooking, shred the cooked chicken into bite-sized pieces. Return the chicken to the pot once the noodles are cooked.
Ladle the soup into bowls, garnish with fresh dill, and serve with lemon wedges on the side.
Enjoy your meal!