Heat the olive oil in a large pot set over medium heat, then add the onions, garlic, salt and pepper and cook until softened and fragrant, about 3 minutes
Pour in ham cooking juices (or bone broth) and water, bring the the boil and then lower the heat, cover loosely and simmer for 60 to 75 minutes, until the beans are tender.
Add the carrots and celery (add a bit more water if necessary) bring back to a simmer and continue cooking until tender, about 10 to 15 minutes.
Throw in the cooked ham and stir well.
Remove from heat and stir in the parsley and thyme; serve without delay.
*If using bone broth, you might want to use a higher ratio of broth to water as it won't be quite as intense in flavor as the ham cooking juices. Just be sure to use a total of 8 cups and go with a ratio that gives you a satisfying flavor.