Place the quinoa and 2 cups water in a small saucepan and bring to a boil. Reduce heat and simmer, covered, until water is absorbed, 12 to 15 minutes.
Meanwhile, heat the oil in a large pot over medium heat.
Add the sweet potatoes and mushrooms and cook, tossing occasionally, until golden and beginning to soften, 5 to 6 minutes.
Stir in the garlic and cook for 1 minute.
Add the kale, wine, ¾ teaspoon salt, and ¼ teaspoon pepper. Cook, tossing often, until the vegetables are tender, 10 to 12 minutes.
Serve the vegetables over the quinoa and sprinkle with the Parmesan.