Ham Bone and Green Split Pea Soup

Ingredients

• 1 teaspoon butter
• 1 teaspoon olive oil
• 4 stalks celery, diced
• ½ large carrot, shredded
• ⅓ white onion, diced
• salt to taste
• 3 cups split peas, rinsed
• 3 cloves garlic, thinly sliced
• 1 ham bone
• 5 cups chicken stock
• 2 cups water, or as needed
• 1 cup diced ham
• ground black pepper to taste