1. Heat olive oil and butter in a large soup pot. Place chicken in the pot and allow to sear for a minute or so on each side. Add a little water if necessary to prevent the chicken from burning.
2. Add chopped onion and cook for several minutes, moving the chicken around, again adding a little water to prevent burning.
3. Add the rest of the vegetables (but not the greens: add them at the end), then add enough water to cover the chicken (about 10 cups). Bring to a boil, skim any foam that rises to the top, and then reduce heat to a simmer. Cook for 50 minutes-1 hour or until chicken is cooked through.
4. Turn off heat. Carefully remove the chicken and allow to cool in a separate bowl.
5. If you are going to serve all of the soup right away, you’ll want to remove the meat from the chicken bones, chop or shred it, and add it back into the soup (make sure you don’t burn yourself). If not serving all of the soup now, you can store the chicken separately and make use of it however you like: I often use some to make chicken salad.
6. Add greens about five minutes before serving: the heat of the soup will wilt them down. Add sea salt and freshly ground pepper to taste.