For sauce, in a small bowl combine chicken broth, oyster sauce, lemon peel, and cayenne pepper; set aside.
In a large nonstick skillet heat 2 teaspoons of the oil over medium heat. Add walnuts and garlic; cook and stir for 2 to 3 minutes or until nuts are lightly toasted. Remove the walnut mixture from the skillet; set mixture aside.
In the same skillet heat the remaining oil over medium-high heat. Add broccoli and sweet pepper; cook and stir for 2 to 3 minutes or until vegetables are crisp-tender.
Stir sauce; add to skillet. Cook and stir for 1 minute. Transfer mixture to serving bowl. Sprinkle with walnut mixture.