In a medium bowl, combine soy sauce, oyster sauce, cornstarch, beef broth, brown sugar, and ground black pepper. Stir until cornstarch is dissolved and set aside.
Place the sliced flank steak and broccoli florets into a large freezer-safe bag or container.
Pour the sauce mixture over the beef and broccoli in the bag or container. Add minced garlic and sesame oil.
Seal the bag or container, removing as much air as possible, and mix gently to coat all ingredients with the sauce.
Label the bag or container with the date and store in the freezer for up to 3 months.
When ready to cook, thaw the freezer meal in the refrigerator overnight.
Heat vegetable oil in a large skillet or wok over medium-high heat.
Add the beef and broccoli mixture to the skillet, including the sauce. Stir-fry for 8-10 minutes or until the beef is cooked through and broccoli is tender-crisp.
Serve hot over steamed rice or noodles if desired.