Heat butter in a large pot over medium-high heat. Add onion and celery and sauté for 2 minutes. Add garlic until fragrant.
Pour in chicken broth and water. Add split peas, bay leaves and thyme. Bring mixture to a boil, then reduce to low. Cover and let simmer, stirring occasionally until peas are tender; about 50 minutes.
Add carrots, potatoes and ham to soup. Cover soup and continue to simmer, stirring until peas have mostly broken down, about 30 mins longer.
Serve, garnish with parsley and enjoy.