In a large nonstick skillet, heat the oil over medium-high heat. Add the mushrooms to the skillet and cook, stirring occasionally, until they begin to brown, about four to five minutes. Add the garlic and cook, stirring, until it becomes fragrant, about 30 seconds. Add the bok choy and snow peas and cook, stirring, until they become bright green, about one to two minutes. Stir in the broth and miso paste and bring the mixture to a simmer. Add the ramen to the skillet and cook, stirring occasionally, until the ramen softens and all of the liquid has been absorbed, about one to two minutes. Stir in the soy sauce.
Serve immediately topped with the green onions or store in the refrigerator for up to five days.