In a large skillet, heat the vegetable oil over high heat until shimmering, about 30 seconds. Add the mushrooms, scallions, bok choy, and carrot and cook, stirring occasionally, until tender, about 5 minutes. Add the garlic, ginger, soy sauce, mirin, and chile-garlic sauce and cook until the liquid has evaporated, about 3 minutes. Season with salt (you won't need much). Transfer the vegetables to a bowl and refrigerate for at least 30 minutes.