Rinse split peas under cold running water until water runs clear. Drain.
Heat oil in a saucepan over medium heat. Add carrot, celery, onion and garlic, and cook, stirring, for 5 minutes or until the onion softens.
Add split peas, ham hocks and water. Bring to the boil over high heat. Reduce heat to medium-low and simmer, covered, for 2 – 2 1/2 hours or until ham hocks are tender and the meat is falling away from the bones. Set aside for 5 minutes to cool slightly. Remove ham hocks from pan. Remove the meat from bones. Coarsely chop meat and set aside.
Place one-quarter of the pea mixture in the bowl of a food processor and process until smooth. Return to pan with ham. Repeat with remaining pea mixture. Taste and season with salt and pepper. Stir over medium-high heat for 5 minutes or until hot.
Ladle soup into bowls and serve immediately with crusty bread.