Prepare the beef by patting the flank steak dry with paper towels, then slicing it thinly against the grain into bite-sized strips.

In a medium bowl, combine the sliced beef with 1 tablespoon soy sauce, 1 tablespoon cornstarch, and 1 teaspoon sesame oil. Toss until the beef is evenly coated, then set aside to marinate while you prepare the other ingredients.

In a separate bowl, whisk together the beef broth, remaining 1 tablespoon soy sauce, oyster sauce, brown sugar, remaining 1 teaspoon sesame oil, minced garlic, and grated ginger until well combined. Set this sauce mixture aside.

Make a cornstarch slurry by stirring together 1 teaspoon cornstarch and 1 tablespoon water in a small bowl until smooth. Set aside to thicken the sauce later.

Rinse and drain the broccoli florets and slice the cremini mushrooms. Pat the vegetables dry so they stir-fry instead of steam.

Heat 1 1/2 tablespoons vegetable oil in a large skillet or wok over medium-high heat until hot but not smoking.

Add the marinated beef to the hot pan in a single layer, cooking undisturbed for 1 to 2 minutes to sear, then stir-fry for another 1 to 2 minutes until just browned but not fully cooked through. Transfer the beef to a plate and set aside.

Add the remaining 1 1/2 tablespoons vegetable oil to the same pan. Add the broccoli florets and stir-fry for 2 to 3 minutes until they begin to turn bright green and slightly tender.

Add the sliced cremini mushrooms to the pan with the broccoli and continue to stir-fry for 2 to 3 minutes until the mushrooms release some moisture and start to brown, and the broccoli is crisp-tender.

Give the prepared sauce mixture a quick stir, then pour it into the pan with the broccoli and mushrooms. Bring it to a gentle simmer over medium heat.

Stir the cornstarch slurry once more, then slowly drizzle it into the simmering sauce while stirring constantly until the sauce begins to thicken and lightly coat the vegetables.

Return the seared beef and any accumulated juices to the pan, tossing everything together so the beef, broccoli, and mushrooms are evenly coated in the thickened sauce.

Season the stir-fry with black pepper and salt to taste, stirring well and cooking for another 1 to 2 minutes until the beef is just cooked through and the sauce clings to all the ingredients.

Remove the pan from the heat and let the stir-fry rest for a minute so the flavors settle, then serve hot while the beef is tender and the broccoli and mushrooms are still vibrant.