Heat the olive oil in a large soup pot over medium heat. Add the diced onion, garlic, carrots, and celery. Cook for about 5–7 minutes, stirring occasionally, until the vegetables are softened and fragrant. This base builds essential flavor for the soup.
Stir in the rinsed split peas, ham bone or diced ham, thyme, and bay leaf. Pour in 7 cups of broth or water. Give everything a good stir and bring the pot to a gentle boil.
Once boiling, reduce the heat to low, cover slightly with a tilted lid, and simmer the soup for 60–75 minutes. Stir occasionally to prevent sticking. The split peas will begin to break down and thicken the soup naturally.
After cooking, the soup should be thick and creamy. For a smoother texture, you can blend part of the soup using an immersion blender. If it becomes too thick, add a splash of water or broth to loosen it.
If using a ham bone, remove it from the pot and shred any remaining meat into the soup. Discard the bone. Taste and adjust seasoning with salt and freshly ground black pepper.
Ladle into bowls and garnish with fresh chopped parsley or crunchy croutons. Serve with crusty bread or a simple salad for a well-rounded meal.