Step 1: Prepare the Base : Rinse the split peas thoroughly and pick out any debris. In a large soup pot or Dutch oven, heat olive oil or butter over medium heat. Add onion, celery, and carrots. Sauté for 5–7 minutes until softened. Add garlic and cook for another 30 seconds until fragrant.

Step 2: Add Broth and Seasonings : Stir in chicken broth, ensuring it covers the vegetables. Add split peas, bay leaves, thyme, black pepper, and smoked ham hock. Bring to a boil, then reduce heat to low and simmer uncovered for 1–1.5 hours, stirring occasionally.

Step 3: Cook Until Creamy : Continue simmering until split peas are tender and the soup is thickened. Remove the ham hock, shred the meat, discard the bone and skin, and return the meat to the soup. Adjust seasoning with salt and pepper.