Prepare the sauce
In a small mixing bowl, combine the honey, soy sauce, grated ginger, minced garlic, and red pepper flakes. Stir well until the ingredients are fully blended.
Marinate the shrimp
Place the cleaned shrimp into a bowl. Pour about one-third of the prepared sauce over them and toss gently so the shrimp are evenly coated.
Thicken the remaining sauce
Add the cornstarch to the remaining sauce mixture and whisk until smooth. Set it aside for later.
Cook the broccoli
Heat a large skillet or wok over high heat. Add the olive oil followed by the broccoli. Season with salt and pepper. Sauté for about 5–6 minutes, stirring occasionally, until the broccoli becomes tender-crisp. Transfer it to a plate and keep it aside.
Cook the shrimp
Melt the butter in the same skillet. Add the shrimp (discard the marinade used for soaking). Cook for about 2 minutes per side, or until the shrimp turn pink and opaque.
Add the sauce
Pour the prepared sauce into the pan with the shrimp. Let it simmer over medium heat for 2–3 minutes, stirring occasionally, until the sauce thickens slightly.
Combine everything
Return the cooked broccoli to the skillet and toss everything together until heated through and coated in the sauce.
Serve
Enjoy immediately over steamed rice or pasta for a quick and flavorful meal.