Rinse the Chinese broccoli thoroughly under cold running water, especially between the leaves and around the stems, to remove any dirt or insects. Drain well. Trim the ends of the stalks, peel any tough outer layer from the thick stems, and cut four small vertical slits into the base of each thick stem. Alternatively, chop the greens into 2-inch-long pieces and thinly slice the thick stalks into smaller pieces on a bias.
Combine the oyster sauce, toasted sesame oil, regular soy sauce, Shaoxing wine, and sugar in a small bowl and whisk well.
Heat the vegetable oil in a large pan over medium heat. Add the minced garlic and fry for 10 seconds until fragrant, making sure it doesn't brown or burn.
Add the prepared Chinese broccoli and water, then stir-fry for 2 minutes, tossing frequently.
Pour in the sauce and toss quickly to coat. Cover immediately and cook for 4-7 minutes, or until the thick stems are crisp-tender and easily pierced with a fork.
Transfer the Chinese broccoli and garlic to a serving plate and pour the remaining sauce over the top. If you left the greens whole, cut them into thirds with kitchen shears before serving.