Tie the parsley stems and thyme together with kitchen string and place in a 6-quart slow cooker. Add the split peas, leek, celery, carrots, 1 teaspoon salt and 1/2 teaspoon pepper; stir to combine. Add the turkey leg and 7 cups water. Cover and cook on low until the split peas and meat are tender, 6 to 8 hours.
Discard the herb bundle. Discard the skin and bones from the turkey leg and shred the meat. Vigorously stir the soup to break up the peas and make the soup smoother. Thin with water, if desired. Stir in the chopped parsley and about three-quarters of the turkey meat; season with salt and pepper.
Ladle the soup into bowls. Thin the yogurt with a little water, then spoon onto the soup. Top with the thawed peas and the remaining turkey. Serve with bread, if desired.