In a large Dutch oven or heavy pot, heat 1 tablespoon olive oil on medium-high. Add the chicken legs and brown on all sides, approximately 2 minutes per side. Remove to a plate.
Add another tablespoon of olive oil to the pot. Add the carrots, celery and green onions, toss together to saute briefly then stir in the garlic. Saute for one minute.
Add the chicken broth and bay leaves then increase the heat to high. Once the liquid has come to a rolling boil, turn down heat and add the chicken. Let simmer for 30-40 minutes until the meat is easy to pull from the bone. Remove the chicken to a plate to cool and remove the meat when cool enough to handle. Discard skin and bones.
Ladle two cups of broth into a bowl and allow to slightly cool slightly while you continue to prepare the soup.
Add the angel hair pasta to the pot. Break strands into approximately one inch long pieces with your fingers over the simmering broth.
Lower heat to a bare simmer and cook for 3-4 minutes until the pasta is done. Add salt and pepper, stir and turn off heat and keep covered.
To prepare the egg-lemon sauce, in a medium bowl, whisk the eggs until thoroughly combined, then add the lemon juice and stir to combine.
Continue to whisk the egg/lemon mixture and slowly add the 2 ladles-full of the broth you set aside. Tempering the eggs with warm broth will make mixing them with the pot of soup less likely result in scrambled eggs!
Once fully combined, slowly add the sauce to the chicken soup and stir continuously. Add the chicken meat to the pot. Heat very gently if necessary.
To serve, garnish with fresh, chopped parsley. Serve hot with your favorite bread. Enjoy!