Soak the bok choy in a large bowl of water for 10 minutes. Tear off the outer leaves and rinse off the dirt. Hold the bok choy stem side up and agitate it to dislodge any remaining dirt and debris. Drain it in a strainer, stem side up, so the water runs out.
Remove the silver skin from the flank steak. Cut the steak against the grain, at an angle, into 1/4-inch slices and put the slices in a bowl.
In a small bowl, stir together 1 tablespoon oyster sauce, 2 teaspoons light soy sauce, 1 tablespoon rice wine, 2 tablespoons water, 1/4 teaspoon white pepper, 1 teaspoon sugar, 1 teaspoon baking soda and 2 tablespoons cornstarch until well combined.
Pour the marinade over the beef and mix lightly for 2 minutes. Set the beef aside in the refrigerator while you prep the rest of the ingredients.
Peel and mince the garlic. Cut the ginger into 1/4-inch slices, then into quarters. Cut the carrot into 1/4-inch slices. Slice the whites off the green onions and halve them; save the green tops for other uses.
Depending on the size of your bok choy, quarter or halve all of it. This helps it cook quickly.
In a small bowl, mix 1 tablespoon oyster sauce, 2 teaspoons light soy sauce, 1/2 teaspoon dark soy sauce, 2 teaspoons rice wine, 1 teaspoon sugar, 1 dash white pepper and, if using, 1 teaspoon chicken bouillon. In a separate bowl, mix 1 teaspoon cornstarch with 1 tablespoon water to make a slurry. Stir 1 tablespoon oil into the marinated beef and set it aside; this helps seal in the juices to keep the meat tender.
Heat a wok on high and add 1 tablespoon oil. When the oil begins to smoke, lower the heat to medium and add half of the minced garlic. Stir fry the garlic for 30 seconds, then add the bok choy and stir fry for 1 to 2 minutes, tossing now and then. Add 1 teaspoon cooking wine and stir fry for another 20 seconds, then add 2 tablespoons water (1 more tablespoon if needed). Cover and steam on low heat for just 40 to 50 seconds. Uncover, toss the bok choy, and add 1/2 teaspoon sugar and 1/2 teaspoon salt. Stir fry to combine, turn off the heat, strain the bok choy and set it aside. Rinse the wok.
Heat the clean wok on high and add the remaining 1 tablespoon oil. When the oil begins to smoke, lower the heat and add the ginger, carrot, green onion whites and the remaining garlic. Stir fry for 1 minute. Raise the heat to medium and add the marinated beef, spreading the pieces out. After 1 minute, flip and stir the beef. Lower the heat, pour in the sauce and stir fry to combine; if it does not look saucy enough, add the cornstarch slurry. Check that the beef has reached 145°F on a food thermometer. Add the bok choy and stir fry everything together for 30 seconds, then stir in 1 teaspoon sesame oil. Lay the bok choy on the bottom of a serving plate and top it with the rest of the stir fry.