In a wok or large skillet, heat 1 tablespoon of oil over high heat until shimmering. Add the mushrooms and sauté until soft, adding a bit of water if necessary. Remove the mushrooms and set aside.
Pour remaining oil into the wok and add the garlic and Brussels sprouts. Stir-fry the vegetables, adding the rice wine, fish sauce, and cooked mushrooms, and continue stirring 15–30 seconds so the liquid can evaporate. Remove from the wok and serve immediately.