In a small bowl or large liquid measuring cup, whisk together the sauce ingredients: soy sauce, water, honey, rice vinegar, sesame oil, and cornstarch. Set near the stove.
In a large skillet or wok, heat the 1 1/2 tablespoons of the canola oil over medium-high heat. Add the shrimp to the skillet in a single layer. Season with the salt and pepper. Cook 1 to 2 minutes per side, until just pink and curling into a "C" (shrimp overcooks fast!). Remove to a plate.
Add the remaining 1 1/2 tablespoons canola oil, then add the broccoli in a single layer. Let it cook undisturbed for 2 minutes.
Stir the broccoli, pour in the water, then cover. Let steam for 2 minutes to soften.
Stir in the garlic, ginger, and white/light green parts of the onions. Toss and cook another 1 to 2 minutes, until the broccoli is crisp-tender.
Pour in the sauce (restir it a bit if it has separated) and add the shrimp. Toss to combine and cook for 1 to 2 minutes, until the sauce is glossy, thickens a bit, and everything is coated.
Sprinkle with the dark green onion parts. Serve immediately over rice with red pepper flakes if you'd like a little heat.
Notes
TO STORE: Refrigerate leftovers in an airtight container for up to 3 days. I don’t recommend freezing this recipe, as the shrimp will be rubbery after freezing, thawing, and reheating.
TO REHEAT: Warm gently in a skillet over medium-low heat or microwave in short intervals until just heated through. Avoid overheating, or the shrimp can become rubbery.