In a small bowl, mix together the soy sauce, oyster sauce, sesame oil, and brown sugar. Set this sauce aside.
Heat a large skillet or wok over high heat. Add a tablespoon of cooking oil and swirl it around to coat the pan.
Add the minced garlic and ginger to the hot pan, and stir-fry for about 30 seconds until fragrant.
Add the sliced beef to the pan and stir-fry for 2-3 minutes until it's no longer pink. Remove the beef from the pan and set it aside.
In the same pan, add a bit more oil if needed and add the sliced mushrooms. Stir-fry for 2-3 minutes until they start to brown and soften.
Toss in the sliced bell peppers and green onions. Continue stir-frying for another 2-3 minutes until the vegetables are slightly tender but still crisp.
Return the cooked beef to the pan and pour the sauce over everything. Stir-fry for an additional 1-2 minutes until the sauce coats the beef and vegetables evenly and everything is heated through.
Serve the Beef Mushroom Stir Fry hot, garnished with white sesame seeds and red pepper flakes if you want a little extra heat.