Step 1: Sort through the 15 bean mix, removing any debris or shriveled beans. Rinse the beans thoroughly under cold running water. Place the rinsed beans in a large bowl and cover with at least 3 inches of cold water. Let them soak overnight (8-12 hours). Alternatively, use a quick soak method: bring beans and water to a boil, boil for 5 minutes, then remove from heat, cover, and let stand for 1 hour. Drain and rinse the soaked beans again, then set aside.
Step 2: In a large stockpot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion, carrots, and celery. Sauté for 8-10 minutes, or until the vegetables are softened and the onion is translucent.
Step 3: Add the minced garlic, bay leaf, and dried thyme to the pot. Cook for another minute until fragrant, stirring constantly to prevent burning.
Step 4: Add the drained beans, smoked ham hock, chicken or vegetable broth, and diced tomatoes (if using) to the pot. Ensure the beans are fully submerged; add more water or broth if necessary. Bring the mixture to a rolling boil.
Step 5: Reduce the heat to low, cover the pot, and simmer for 2-3 hours, or until the beans are tender. Stir occasionally to prevent sticking. The cooking time may vary depending on the freshness and type of beans.
Step 6: Once the beans are tender, carefully remove the ham hock from the pot. Allow it to cool slightly, then shred the meat from the bone, discarding any skin, fat, or gristle. Return the shredded ham to the soup.
Step 7: Taste the soup and season generously with salt and freshly ground black pepper. If the soup is too thin for your liking, you can mash a portion of the beans against the side of the pot with a spoon or use an immersion blender to thicken it slightly (be careful not to over-blend).
Step 8: Ladle the hearty 15 bean soup into bowls. Garnish with fresh chopped parsley or cilantro, and serve hot with crusty bread or cornbread on the side.