In a small bowl, mix together the soy sauce, oyster sauce, cornstarch, and water. Stir until the cornstarch is fully dissolved. Set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the minced garlic and ginger, stirring for about 30 seconds until fragrant.
Add the shrimp to the skillet and cook for about 3-4 minutes, or until they turn pink and are cooked through. Remove the shrimp from the skillet and set aside.
In the same skillet, add the broccoli florets and sauté for 3-4 minutes until they are bright green and slightly tender.
Return the cooked shrimp to the skillet with the broccoli. Pour the sauce over the shrimp and broccoli. Stir well to coat everything in the sauce.
Cook for an additional 2-3 minutes until the sauce thickens slightly and everything is heated through. Season with salt and pepper to taste.
Serve immediately over cooked rice or quinoa if desired.