Trim any excess fat from the steak. Cut against the grain into about 1-inch pieces. Place the steak pieces in a mixing bowl and stir in the pepper and ¼ cup soy sauce.
Stir in the egg, 2 tablespoons cornstarch and 2 tablespoons olive oil. Cover and let rest for at least 30 minutes.
Add the carrots and broccoli to a pot and cover with water. Bring to a light boil just until the vegetables are tender, about 5 to 10 minutes. Drain and set aside.
Meanwhile, preheat a wok or large cast iron skillet over medium-high heat. Add 2 tablespoons olive oil, bell peppers and meat. Cook for about 3 to 4 minutes or until the meat has lightly browned and the peppers are al dente, stirring frequently. Remove the contents of the skillet and place in a warm skillet.
Drain the broccoli and carrots well and add to the wok. Cook over medium-high heat until the broccoli just begins to brown, about 4 minutes, stirring frequently. Remove and place with the meat mixture.
Return to the wok and add 1 tablespoon olive oil, oyster sauce, ¼ cup of soy sauce, ginger, and garlic, Cook for about 2 minutes, stirring frequently.
Stir in the meat and veggie mixture until combined. Stir in the red wine and cook for about 2 to 3 minutes to allow the flavors to incorporate, stirring frequently.
Remove from the wok and serve over rice.