1. Combine shrimp and cornstarch in a medium bowl, tossing to coat. Heat a large wok or skillet over high heat. Add 1 tablespoon oil to pan; swirl to coat. Add shrimp; stir-fry 4 minutes. Remove shrimp from pan; place in a medium bowl. Add 1 1/2 teaspoons oil to pan; swirl to coat. Add green onions, ginger, and garlic to pan; stir-fry 45 seconds. Add onion mixture to shrimp.
2. Add 1 tablespoon oil to pan; swirl to coat. Add broccoli; stir-fry 1 1/2 minutes. Stir in shrimp mixture, soy sauce, and remaining ingredients; bring to a boil. Cook 1 minute or until shrimp are done and broccoli is crisp-tender.