1. Heat oil in a 6-quart pot over moderate heat. Add leeks, carrots, and celery, season with salt and pepper, and cook, stirring, until softened, about 5 minutes. Add garlic and cook, stirring, 1 minute. Add 3 quarts water and remaining ingredients; simmer, loosely covered, until split peas are very tender, about 1 hour.
2. Remove and discard bay leaf and thyme sprigs. Transfer ham hock to a cutting board. Puree soup in small batches in blender until smooth. Transfer to a clean pot. Remove skin and fat from ham hock. Pull meat from bone and shred into bite-size pieces. Add 3/4 of ham to soup and reheat over moderate heat, stirring occasionally; salt and pepper to taste.
3. To serve, ladle soup into bowls and garnish with remaining ham. Makes 8 servings.