Make broth. Place the bone from the ham you smoked and place it in a large stockpot or Dutch oven. Add enough water to cover the bone to about halfway, about 6-7 cups. Bring the water to a boil, reduce the heat, and simmer until very fragrant. This should take about 30 minutes to 1 hour. Set aside your ham stock and discard the bone.
Cook ingredients. Heat olive oil in a large Dutch oven or pot over medium heat. Add garlic, onion, carrots, and potato. Cook them stirring occasionally until onions have become translucent, about 2-3 minutes. Stir in ham stock, corn, thyme, and bay leaves. Season with salt and pepper, to taste.
Boil. Bring to a boil and then reduce to a simmer. Cook until the potatoes are tender, about 10-12 minutes. Stir in ham until heated through, about 1-2 minutes.
Serve. Once ready, serve hot with fresh bread.