In a large stock pot, heat olive oil until shimmering. Working in batches, brown the chicken skin side down (do not cook all the way through). Set chicken aside.
Sautee the onions and ginger until softened.
Add the chicken to the onions in the pot. Add soy and fish sauce and mix around.
Add water until chicken is just covered.
Cover the pot and bring to a rolling boil. Let boil for 5 minutes, then reduce temperature and allow to simmer for about 1 hour or until the meat is tender and starts to release from the bone.
Add the tinola seasoning mix, cucumber, and green beans. Mix well. Bring to a low boil, cover the pot, and allow to boil until the vegetables have softened.
Turn off the heat. Add the leafy greens to the pot and cover. Allow the greens to wilt in the steam for a few minutes.
Serve with fresh jasmine rice.