Start by preparing the ingredients. Peel and devein the shrimp if you haven't done so already. Wash and cut the broccoli into small florets.
In a small bowl, mix the soy sauce, cornstarch, chicken broth, and sesame oil. Set aside.
Heat the vegetable oil in a wok or large skillet over medium-high heat.
Add minced garlic and grated ginger to the pan, stirring for about 30 seconds until fragrant.
Add the shrimp to the wok and cook for about 3-4 minutes, or until they turn pink and are cooked through. Remove the shrimp and set aside.
In the same wok, add the broccoli florets and stir-fry for about 2-3 minutes until they are tender-crisp.
Return the shrimp to the pan and pour the soy sauce mixture over the shrimp and broccoli. Stir well to combine and cook for another 2 minutes, allowing the sauce to thicken slightly.
Season with salt and pepper to taste.
Serve hot over cooked rice or noodles if desired.