In a Dutch oven or heavy saucepan, heat the butter over medium heat. Add onion, carrots, leeks, celery, garlic, salt and pepper. Cook until veggies are soft and fragrant, about 5 minutes. Add the ham bone (if using), split peas, bay leaves, chicken broth (or stock), water and ham. Set to medium-high heat and bring to a boil. Reduce to medium-low and simmer uncovered for 1 hour (stirring occasionally), or until peas are soft and broken.