Place the dried navy beans in a large bowl and cover them with several inches of cool water. Let them soak on the counter for at least 6 hours, or overnight.
If you are short on time, use the quick soak method instead: boil the beans in water for 2 minutes, then remove from heat and let them sit, covered, for 1 hour. Drain and rinse the soaked beans before using them in the recipe, and set them aside.
Place the ham bone in your Dutch oven or stockpot and add the 8 cups of water or water and broth mixture. Add one of the bay leaves and bring the pot to a gentle boil over medium high heat.
Once boiling, reduce the heat to low, cover, and let it simmer for 45 minutes to 1 hour so the bone releases its flavor into the liquid. Remove the ham bone from the pot and set it on a plate to cool slightly, but keep the broth in the pot.
While the bone simmers, or right after you remove it, push the broth to one side or ladle it into a separate bowl temporarily. Heat the olive oil in the same pot over medium heat.
Add the diced onion, carrots, and celery, and cook for 5 to 7 minutes, stirring occasionally, until the onion turns soft and translucent. Stir in the minced garlic and cook for another 30 seconds, just until fragrant.
Pour the reserved ham broth back into the pot with the sautéed vegetables. Add the drained, soaked navy beans, the remaining bay leaf, dried thyme, and black pepper.
Bring the soup back up to a gentle boil, then reduce the heat to low, cover, and simmer for 60 to 75 minutes, stirring occasionally, until the beans are tender. Check the beans for doneness around the 60 minute mark, since older dried beans can take longer to soften.
While the broth simmers, remove any remaining meat from the cooled ham bone and shred or chop it into bite sized pieces. Once the beans are almost tender, stir the diced potatoes into the pot.
Continue simmering, uncovered, for 15 to 20 minutes, until the potatoes are fork tender. Stir in the shredded ham from the bone along with the extra diced leftover ham, and heat through for about 5 minutes.
Discard both bay leaves from the pot. Taste the soup and add salt as needed, keeping in mind that ham can already be quite salty. Ladle the hot soup into bowls and top with freshly chopped parsley.
Serve immediately while warm, with crusty bread or cornbread on the side.