In a large pot or Dutch oven, heat olive oil (optional) over medium heat. Add the diced onion, carrots, celery, and garlic. Sauté for about 5 minutes, or until the vegetables start to soften.

Add the ham bone to the pot along with the rinsed split peas, bay leaves, thyme, and black pepper.

Pour in the water or chicken broth, ensuring the ham bone is submerged. Stir to combine.

Bring the soup to a boil over high heat, then reduce the heat to low and let it simmer uncovered for 60-90 minutes, stirring occasionally.

Once the peas are soft and the soup has thickened, remove the ham bone from the pot. Let it cool slightly, then shred any remaining meat off the bone and return the meat to the soup. Discard the bone.

Taste the soup and adjust seasoning, adding salt if needed. If the soup is too thick, add additional water or broth to reach your desired consistency.

Remove the bay leaves before serving. Ladle the soup into bowls and enjoy warm.