In a small bowl, whisk together soy sauce, honey, rice vinegar, cornstarch, sesame oil, pepper, and red pepper flakes or chili oil (if using) until smooth. Set aside.
Heat the oil in a large skillet or wok over medium-high heat. Add broccoli and red bell pepper and stir-fry for 3-4 minutes, until the broccoli is bright green and just tender and the pepper is slightly softened. Transfer the vegetables to a plate.
Pat shrimp dry with paper towels and add to the same skillet in a single layer. Cook for 2 minutes per side, until just pink and lightly golden. Remove the shrimp from the skillet and set aside with the vegetables.
Reduce the heat to medium. Add garlic and ginger to the skillet and cook for 30 seconds, stirring constantly, until fragrant. Return the shrimp and vegetables to the skillet.
Give the sauce a stir and pour it in. Toss for 1-2 minutes, until the sauce thickens and coats the ingredients.
Serve over rice and finish with sliced green onions and freshly cracked black pepper.
Notes
If you want the broccoli extra tender and bright green, you can blanch them in hot water before cooking them - just make sure to dry them well.
Frozen shrimp should be thawed all the way and patted dry before cooking. Excess moisture will prevent them from searing properly and can make the sauce thinner.
Shrimp go from perfect to overcooked quickly, so pull them from the skillet as soon as they turn opaque. Otherwise, they can become rubbery and tough.
Store leftovers in an airtight container in the fridge for up to 2 days. Reheat in a skillet over low heat, adding a little water if needed to loosen the sauce, just until warmed through.
Serve this stir fry with rice or noodles, or keep it simple and enjoy it as is.