Wash the quinoa very well in a fine-mesh strainer; drain. Melt 1 tablespoon butter in a saucepan over medium-high heat and add the quinoa, toasting it for 1-2 minutes. Add 2 cups of water and a pinch of salt. Bring to a boil; then reduce heat to low, cover and cook for 15 minutes. Take the pan off the heat and let sit for another 5 minutes without lifting the lid.
Meanwhile, melt a teaspoon of butter in a sauté pan over medium-high heat. Once it starts to foam, add the tatsoi and a pinch of salt and cook until bright green and slightly wilted. Set aside on a large plate. Melt another teaspoon of butter in the sauté pan and add the eggplant with a pinch of salt, cooking until very soft and golden brown (add more butter to the pan if it dries up); set aside on the plate. Melt one more teaspoon of butter in the sauté pan and add the mushrooms and a pinch of salt. Cook until dark brown and tender; set aside on the plate.
Whisk together the lime juice, soy sauce, rice vinegar, sesame oil, ginger and sugar. Divide the quinoa between two bowls, top with the vegetables and drizzle with the dressing. Garnish with scallions and sesame seeds.