Heat olive oil or butter in a large stockpot or Dutch oven over medium heat (optional). Add diced onion, carrots, celery, and garlic. Sauté for 5-7 minutes until softened and fragrant.

Rinse the split peas thoroughly under cold water and set aside.

Add the ham bone to the pot, followed by the rinsed split peas, chicken or vegetable broth, bay leaves, dried thyme, and ground black pepper.

Bring the soup to a boil over medium-high heat, then reduce the heat to low and let it simmer uncovered for 1.5 to 2 hours, stirring occasionally to prevent the peas from sticking to the bottom.

After the cooking time, remove the ham bone and let it cool slightly. Shred any remaining meat from the bone and return the meat to the pot.

Discard the bay leaves and stir the soup well. If the soup is too thick, add more broth or water to reach your desired consistency.

Taste and adjust seasoning with salt and additional pepper, if needed.

Serve the split pea soup hot, garnished with crusty bread or a sprinkle of fresh parsley, if desired.