In a medium bowl, mash the beans with a fork. Add the quinoa, sweet potatoes and kale, eggs, Parmesan, ½ teaspoon salt, and ¼ teaspoon pepper and mix to combine. Dividing evenly, form the mixture into twelve 3-inch patties (about ½ cup each).
Heat 1 tablespoon of the oil in a large nonstick skillet over medium heat. In batches, cook the patties until browned and cooked through, 3 to 4 minutes per side (adding more oil if necessary).
In a large bowl, whisk together the vinegar, the remaining 2 tablespoons of oil, and ¼ teaspoon each salt and pepper. Add the greens and tomatoes and toss to combine. Serve with the quinoa and bean patties.