Blot shrimp with a paper towel to dry and place in a medium bowl with cornstarch. Toss to coat.
Heat a large wok or skillet over high heat. Add 1 tablespoon oil and shrimp to pan; stir-fry about 4 minutes, or until golden brown. Do not over cook.
Remove shrimp from pan. Add 1 1/2 teaspoons oil and stir-fry green onions, ginger, and garlic for 45 seconds. Remove from pan and add to the shrimp.
Add the remaining 1 tablespoon oil to pan and stir-fry broccoli for 1 1/2 minutes. Stir in shrimp and onion mixture to pan. Pour in soy sauce, rice vinegar, honey, and red pepper flakes and bring to a boil. Cook just 1 minute or until broccoli is crisp-tender.