Drop garlic through food chute with food processor on; process until minced. Add parsley and next 4 ingredients; process until finely minced. Gradually add olive oil and 1 tablespoon water, processing just until blended.
. Bring 2 quarts water to a boil in a 4-quart saucepan. Add broccoli, and cook 2 minutes. Remove 2 cups gnocchi from package; reserve remaining gnocchi for another use. Add gnocchi to pan, and cook 3 minutes or just until broccoli is tender; drain and place in a large bowl. Add chicken and parsley mixture; toss gently to coat. Sprinkle with 2 tablespoons walnuts and 2 tablespoons Parmesan cheese, if desired.