In a pot over medium heat, heat about 1 tablespoon of oil. Add beef shank and cook on both sides until lightly seared. Remove from pot and set aside.
Add water to the pot and bring to a boil. Return beef shanks and continue to boil, skimming scum that floats on top.
When the broth has cleared, add onions, garlic, peppercorns, and salt. Lower heat, cover, and simmer for about 1 1/2 to 2 hours or until meat is tender.
In a wide pan, heat about 1 tablespoon of oil. Add bananas and cook, turning on sides as needed, until lightly browned. Remove from pan and set aside.
Add chorizo de bilbao. Cook, turning as needed, for about 1 to 2 minutes or until chorizo de bilbao releases color. Remove from pot and set aside.
Add another tablespoon of oil if needed. Add chicken and cook, turning on sides, until lightly browned. Remove from pot and drain on paper towels.
Add chicken, ham, and chorizo de bilbao to the pot and cook, skimming scum that floats on top, for about 15 to 20 minutes or until chicken is cooked through.
Add garbanzo beans and saba bananas and cook for about 3 to 5 minutes or until heated through.
Add green beans and cabbage and cook until tender yet crisp.
Add pechay and cook for another 1 minute. Season with additional salt as needed.
To serve, arrange meat and vegetables on a serving platter. Transfer broth into a serving tureen. Serve hot with berenjana sauce.