Steam broccoli, covered, 2 minutes or until crisp-tender; rinse with cold water. Drain; cool.
Combine eggs and 2 tablespoons water. Heat 1 teaspoon vegetable oil in a large nonstick skillet or wok over medium-high heat. Add egg mixture; stir-fry 30 seconds or until soft-scrambled, stirring constantly. Remove egg mixture from pan.
Add 2 teaspoons vegetable oil to pan. Add ginger and garlic; stir-fry 30 seconds. Add rice; stir-fry 3 minutes. Add broccoli, carrot, and broth; cook 1 minute. Add cooked eggs, soy sauce, sesame oil, and salt; stir-fry 1 minute or until thoroughly heated. Sprinkle with green onions.