For filling, in a 2-quart saucepan combine rice and broth; bring to boiling. Reduce heat and simmer, covered, 15 minutes.
Meanwhile, cut tops off small peppers, or halve large peppers lengthwise. Remove membranes and seeds. In a 4-quart Dutch oven immerse peppers in boiling water oven for 3 minutes. Remove; drain, cut sides down, on paper towels. Place in a serving dish cut side up. Sprinkle lightly with salt and black pepper; set aside.
With a vegetable peeler, shave 1 ounce of the Parmesan in thin strips; set aside. Finely shred or grate the remaining Parmesan; set aside. Stir asparagus or broccoli, chicken, and herb into rice. Cover and cook 5 minutes more. Stir in whipping cream, shredded or grated cheese, and nuts. Spoon filling into peppers. Top with shaved cheese. Makes 4 servings.