In a small bowl, mix soy sauce, oyster sauce, brown sugar, and black pepper. Set aside.
In another bowl, dissolve cornstarch in water to make a slurry.
Heat 1 tablespoon of oil in a large skillet over medium-high heat.
Add broccoli and stir-fry for 3-4 minutes until crisp-tender. Remove and set aside.
Add remaining oil and garlic to the skillet. Stir-fry beef slices until browned, about 3-5 minutes.
Return broccoli to the skillet and pour in the sauce mixture.
Add cornstarch slurry and stir everything until the sauce thickens, about 1-2 minutes.
Serve hot over steamed rice or noodles.