Submerge the split peas in water in a bowl, remove small stones.
Heat oil in 5 litre (6 qt) saucepan set to low-medium heat. Add onions, and cook for 15 minutes, or until dark brown, stirring occasionally.
Add carrots, celery, and garlic and cook for 2 minutes.
Add remaining ingredients. Add additional water or chicken stock as required. Bring to boil and set to simmer for 1 hour.
Remove ham bones to cutting board and cut meat and fat into 1 cm (1/2 inch) cubes and return to pot, include bone. Simmer for 1 hour.
Remove bay leaf. Add salt to taste – check first – the ham may provide sufficient salt flavour. If desired, add additional chopped garlic before serving.