In a medium bowl, combine the sliced beef, soy sauce, and cornstarch. Mix well and let it marinate for about 15 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated beef and stir-fry for about 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the minced garlic and ginger, and stir-fry for about 30 seconds until fragrant.
Add the chopped bok choy, sliced red bell pepper, and julienned carrot to the skillet. Stir-fry for 3-5 minutes until the vegetables are tender-crisp.
Return the cooked beef to the skillet. Pour in the oyster sauce and sesame oil, and toss everything together until well combined. Season with salt and pepper to taste.
Serve the stir-fried beef and bok choy over cooked rice.