Thaw the shrimp completely and pat the surface dry. You may also need to remove the shell, tail, and veins.
Combine sauce ingredients except for the cornstarch/water and set aside.
Cook the Shrimp: Heat olive oil in a large skillet over medium-high heat. Add the shrimp and cook for about 1 minute + 20 seconds per side. (Use a timer to avoid overcooking). Tilt the pan to transfer the shrimp onto a clean plate. Note that they’ll cook a little bit more as they sit, and again when added back to the sauce.
Add the broccoli to the skillet and sauté over medium-high heat for 4 minutes, until slightly softened. (Add a splash of oil if needed). Remove and set aside.
Make the Sauce: Add the sauce mixture (minus the cornstarch) to the skillet.
Combine cornstarch with ¼ cup cold water and stir until well-combined.
Bring the sauce to a boil. Slowly add the cornstarch mixture to the sauce, stirring continuously, until thickened.
Reduce heat to low and add the broccoli. Cover partially and let it heat for 2-3 minutes.
Add the shrimp back and spoon the sauce on top. Let it heat through for about 1 minute.
(Optional: Transfer to serving plates and drizzle with honey!) Serve with rice and garnish with green onions and roughly chopped honey roasted peanuts.