Rinse the bok choy. If they are rather large, split lengthwise vertically.
Remove and discard the mushroom stems. Cut the caps into thick slices.
In a shallow pan, bring the vegetable broth to a boil. Add the bok choy and cook over high heat for two to three minutes. The actual cooking time depends on the size of your bok choy. You want to cook them just until the leaves wilt. Scoop out, let drip then arrange on a serving plate.
In a wok or frying pan, heat the oil. Add the garlic and mushrooms. Sprinkle in the salt, pepper and sugar. Stir fry the mushrooms and garlic for about half a minute. Pour in the rice wine and two tablespoons of the vegetable broth in which the bok choy was cooked. Cook for two minutes. Scoop out the mushrooms and pile on top of the bok choy.
To the remaining liquid in the wok or frying pan, add the vegetarian oyster sauce. Heat until simmering. If too thick, add another tablespoon of broth. Turn off the heat. Drizzle in a little sesame seed oil and stir.
Spoon the sauce over the mushrooms and bok choy. Garnish with sesame seeds.
Serve the bok choy and mushrooms in oyster sauce as a side dish or as a vegan main dish.