Combine honey soy sauce garlic and grated ginger in a small bowl and whisk until smooth.
Warm olive oil in a skillet over medium heat and arrange shrimp in a single layer. Let them cook for 2 to 3 minutes on each side until they turn pink and form a C shape; avoid overcooking.
Pour the honey garlic sauce into the skillet with the shrimp and let it simmer for around 2 minutes until it thickens into a shine glaze, stirring carefully to coat all the shrimp.
Meanwhile, steam or sauté broccoli florets until they are just tender and bright green, adding a touch of caramelization if desired.
Serve bowls by spooning cooked rice or quinoa into each, topping with the honey garlic shrimp and veggies. Sprinkle green onions and optionally some sesame seeds or red pepper flakes to finish.