Heat the olive oil in a large heavy soup pot over medium heat.
Add the onion, carrots and celery and cook for 6–8 minutes, stirring occasionally, until the vegetables begin to soften. Add the garlic and cook for another minute.
Add the bay leaves, thyme, split peas and ham bone. Pour in the water or broth and give everything a good stir.
Bring the soup to a boil, then reduce the heat to low and simmer gently, partially covered, for approximately 1½–2 hours, stirring occasionally, until the split peas have broken down and the ham is tender.
Remove the ham bone, bay leaves and thyme stems from the pot. When the ham is cool enough to handle, pull the meat from the bone, discard the bone and any excess fat, and shred or chop the meat into bite-sized pieces.
Use an immersion blender to partially blend the soup. You don’t want to puree it, just blend enough to make it a bit more creamy.
Return the ham to the soup and stir well.
To make the chili garlic butter, melt the butter in a small saucepan over medium-low heat. Add the garlic and red pepper flakes and cook gently for 30–60 seconds, just until fragrant. Be careful not to burn the garlic. Add a few grinds of black pepper and remove from the heat.
Ladle the hot soup into bowls and spoon the chili garlic butter over the top. Finish with a generous amount of finely grated Parmesan, fresh parsley and more freshly ground black pepper.