If you're using dried beans or a dried bean mix, you need to soak the beans for 8-10 hours first. To do this just cover the dry beans with a few inches of cold water and leave them on the kitchen counter for the time needed. Drain and rise the beans when done soaking.
Get your ingredients ready. Chop and dice the potatoes into bite-sized chunks, chop the rest of the veggies. Mince the garlic.
In a heavy soup or stock pot, melt oil or fat and saute carrots, celery, and onion until soft, 8-10 minutes. Then add garlic and bay leaf and stir for 60 seconds. Add a pinch of salt and freshly cracked black pepper.
Add the ham bone and the drained beans. Cover with water so that the bone is submerged by 2 inches, and bring to a boil before reducing heat to a simmer. Cover the pot and allow to cook for 2 to 2.5 hours.
After two hours, uncover pot, add the tomatoes and potatoes. Simmer until potatoes are tender, about 30 minutes.
Taste for salt and pepper and adjust. Continue simmering until beans are tender and ready.
Add more water to adjust for liquid evaporation and to adjust for thickness to your liking. Remove bone, stir in leftover ham meat scraps, and serve hot with rustic crusty bread on the side. I always serve this with sourdough breads like rye and I love to garnish it with fresh parsley right at the end.