1. Heat a wok or large frying pan over high heat. Add 2 tbsp. oil and swirl wok to coat. Cook bok choy stems and carrots, stirring often until starting to soften, about 3 minutes. Add red pepper and cook another 2 minutes. Transfer mixture to a bowl.
2. Return wok to heat and add remaining 1 tbsp. oil. Add bok choy leaves and mushrooms. Cook, stirring once or twice to prevent burning, until leaves are starting to soften, about 2 minutes more. Add remaining ingredients and reserved vegetables, stirring to combine.