Mix together oyster sauce, soy sauce, and brown sugar in a medium bowl until sugar is dissolved. Mix together water and potato starch in a small bowl until smooth; stir into oyster sauce mixture until well combined. Set aside.

Fill a large pot with water and bring to a boil. Stir in vegetable oil and 2 pinches salt. Place bok choy into boiling water; cook until tender, shiny, and bright green, 2 to 3 minutes. Drain and arrange bok choy attractively on a serving platter.

Heat olive oil in a large skillet or wok until shimmering. Cook and stir green onion and garlic in hot oil until fragrant, about 20 seconds; stir in mushrooms. Cook and stir until mushrooms begin to shrink slightly. Sprinkle lightly with salt. Continue to cook mushrooms, stirring often, until tender, about 5 minutes. Pour in oyster sauce mixture and stir until sauce is thickened and coats mushrooms, 30 seconds to 1 minute. Pour mushroom sauce over bok choy on the platter. Serve hot.