Heat 2 tbsp. oil in a wok or large frying pan over high heat. Add brussels sprouts and onion and cook 3 minutes. Drain mushrooms and squeeze out any excess liquid, then add to wok. Cook, stirring occasionally, until onion starts to soften and brussels sprouts are bright green, about 3 minutes. Add garlic and cook until fragrant, about 2 minutes. Stir in seasonings and broth and cook until most of liquid is gone, about 3 minutes.