- Heat vegetable oil in a large skillet or wok over medium-high heat. Add minced garlic and ginger, sauté for about 30 seconds until fragrant. 
- Add the shrimp to the skillet and cook for 2-3 minutes until they turn pink and opaque. Remove shrimp from the skillet and set aside. 
- In the same skillet, add broccoli florets and stir-fry for about 3-4 minutes until they are bright green and tender-crisp. 
- In a small bowl, mix soy sauce, oyster sauce, cornstarch, and water until smooth. Pour the sauce over the broccoli and stir well. 
- Return the shrimp to the skillet, add sesame oil, and stir everything together. Cook for an additional 2 minutes until the sauce thickens slightly. Season with salt and pepper to taste. 
- Serve hot over cooked rice or noodles.