Gumbo zHerbes with Perfect Rice

Name: Gumbo z'Herbes with Perfect Rice
Ingredients: 11 tablespoons vegetable oil, divided; 4 cups 1/2-inch cubes smoked ham (about 22 ounces); 2 tablespoons (1/4 stick) butter; 6 cups sliced leeks (white and pale green parts only; from 5 large); 2 cups finely chopped celery; 2 cups sliced green onions (about 8); 1 cup chopped fresh Italian parsley; 5 large garlic cloves, chopped; 3 tablespoons filé powder*; 1 tablespoon chopped fresh oregano; 3 /4 teaspoon cayenne pepper; 8 cups sliced collard greens (about 6 ounces); 8 cups sliced mustard greens (about 6 ounces); 1 large bunch watercress, thick stems trimmed (about 4 cups); 4 cups fresh spinach leaves; 1 /2 teaspoon sugar; 10 cups low-salt chicken broth, divided; 3 /4 cup all purpose flour; Perfect Rice (click for recipe)