To a medium sauté pan, set over medium heat, heat the sesame oil. When hot, add the swiss chard stems and green onions; cook until slightly softened, about 2 minutes. Mix in the minced garlic, grated ginger, red chile pepper and cook for an additional minute, until the garlic is fragrant—it should start to smell awesome. Pour in the soy sauce, mirin, swiss chard leaves, mushrooms and sesame seeds; give it a good mix and cook for an additional minute or two until the vegetables have softened. Squeeze in the lime juice, turn the heat down to low and cover.