Make the Sauce: Add the soy sauce, chicken broth, oyster sauce, honey or brown sugar, cornstarch, sesame oil, and black pepper to a bowl, then whisk until the mixture is well combined and the cornstarch is incorporated.
Prepare the Stir-Fry Ingredients: Have the shrimp, broccoli, minced garlic, grated ginger, vegetable oil, and prepared sauce ready before beginning to cook, since the stir-frying process moves quickly.
Cook the Shrimp: Heat part of the divided vegetable oil in a large wok or pan, add the shrimp, and cook until they turn pink and opaque. Avoid overcooking, then remove the shrimp from the pan and set them aside. Cook the Broccoli: Add the remaining vegetable oil to the pan, then cook the broccoli until it reaches the desired crisp-tender texture while allowing enough room in the pan to prevent overcrowding.
Add the Aromatics: Add the minced garlic and grated ginger to the pan and stir them with the broccoli until fragrant.
Combine the Sauce: Whisk the prepared sauce again if needed, then pour it into the pan with the broccoli and aromatics, stirring as it heats and begins to thicken.
Return the Shrimp: Add the cooked shrimp back to the pan and toss everything together so the sauce coats the shrimp and broccoli evenly.
Finish the Stir-Fry: Allow the sauce to simmer until it reaches the desired consistency; if it becomes too thick, loosen it with a splash of broth, or simmer for another 30–60 seconds if a thicker sauce is preferred.
