Rinse dried lima beans thoroughly. Place them in a large bowl, cover with at least 3 inches of cold water, and soak overnight (8-12 hours). Drain and rinse before use. (Alternatively, quick soak: bring beans and water to a boil, boil 2 minutes, cover, remove from heat, let stand 1 hour, then drain and rinse.)

In a large Dutch oven or heavy-bottomed pot, heat 1 tablespoon of olive oil over medium-high heat. Add the ham hocks and brown them on all sides for about 5-7 minutes.

Add the roughly chopped initial onion, carrots, and celery to the pot with the ham hocks. Sauté for 5 minutes until slightly softened.

Pour in 8 cups of water (or chicken broth) and add the bay leaves. Bring to a boil, then reduce heat to low, cover, and simmer for 1.5 to 2 hours, or until the ham hocks are very tender and the meat is easily falling off the bone.

Carefully remove the ham hocks from the pot using a slotted spoon and set aside to cool slightly. Discard the bay leaves and the cooked initial vegetables from the broth using the slotted spoon or a fine-mesh sieve. Strain the broth if desired for a clearer base, but it's not strictly necessary. Return the pot with the clear broth to the stovetop.

Once cool enough to handle, remove the skin, bones, and any excess fat from the ham hocks. Shred the tender ham meat into bite-sized pieces. Set aside.

Heat the remaining 1 tablespoon of olive oil in the same Dutch oven over medium heat. Add the finely diced onion, carrots, and celery. Sauté for 8-10 minutes until softened.

Add the minced garlic, dried thyme, smoked paprika, and red pepper flakes (if using). Cook for another 1 minute until fragrant.

Add the drained and rinsed lima beans to the pot. Pour in the reserved ham hock broth. Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 45-60 minutes, or until the lima beans are very tender. Stir occasionally to prevent sticking.

Once the beans are tender, use the back of a spoon or a potato masher to mash about 1/4 to 1/3 of the beans against the side of the pot. This will thicken the soup and create a creamy texture.

Stir the shredded ham hock meat back into the soup. Heat through for 5 minutes.

Taste the soup and season generously with salt and freshly ground black pepper. Adjust seasonings as needed. If the soup is too thick, add a bit more vegetable or chicken broth or water to reach your desired consistency.

Ladle the hearty lima bean soup into bowls. Garnish with fresh chopped parsley, if desired, and serve hot with crusty bread or cornbread.