Heat oil and butter in a heavy pot over medium heat.
Add onions and salt; cook slowly until deeply golden.
Stir in garlic and cook until fragrant.
Add balsamic vinegar, Worcestershire-style sauce, and broth with lemon juice.
Add seasonings, bay leaves, beans, broth, and chicken.
Bring to a gentle boil, then simmer for 20 minutes.
Remove bay leaves, adjust seasoning, and serve hot.
