Rinse the quinoa in a strainer under cold running water and drain well. Heat a heavy saucepan over high heat and toast the quinoa for about 5 minutes, stirring constantly with a spatula and scraping the bottom of the pan so that the grains do not scorch. Transfer the quinoa to a large saucepan and add the water. Over medium high heat, bring the water to a boil, reduce the heat to low, cover, and cook for about 10 minutes, or until all the water has been absorbed. Remove from the heat and allow to cool.

In a large bowl, combine the quinoa, flour, Parmesan, salt, and pepper. Mix thoroughly and add the green onions, parsley, egg, and egg yolk. Blend together thoroughly until the mixture has the consistency of a soft dough.

In a large, heavy skillet, heat the oil over medium heat. Using 2 soup spoons, shape the mixture into egg shapes and drop them gently into the hot oil. Cook, turning over once the croquettes are firm and golden on the bottom, until all the croquettes are golden on all sides (about 1 minute total). Drain briefly on paper towels and serve with lemon wedges.