Slice the beef against the grain into thin strips. Toss with 2 tablespoons soy sauce and 1 tablespoon cornstarch. Let marinate for 10-15 minutes while preparing vegetables.
Heat 1 tablespoon oil in a large skillet or wok over medium-high heat until shimmering. Add beef in a single layer and cook 2 minutes per side until browned. Remove to a plate.
Add remaining oil to the pan. Add bell peppers and onion, stir-frying for 3-4 minutes until tender-crisp. Add garlic and ginger, cooking 30 seconds until fragrant.
Whisk together 3 tablespoons soy sauce, oyster sauce, brown sugar, black pepper, and beef broth. Pour into the pan with vegetables and simmer 2 minutes.
Return beef to the pan with any juices. Stir the cornstarch slurry and add to the pan. Cook 1-2 minutes until sauce thickens and coats everything.
Serve immediately over hot rice. Garnish with sliced green onions and sesame seeds if desired.