Place a small, dry saucepan over heat. Add quinoa and toast for roughly 5 minutes, shaking and stirring constantly so the quinoa doesn't scorch. Transfer to a large saucepan and add water. Bring to a boil, reduce to a simmer and cook, covered, until water is absorbed, about 10 minutes. Set aside to cool.
In a large bowl, combine cooked quinoa, flour, cheese and salt. Add onions, parsley, egg and yolk. Stir thoroughly with a spoon until the mixture has the consistency of soft dough. Chill the dough for 30 minutes
Heat oil in a large skillet over medium heat.
In a small mixing bowl, season avocado with salt and pepper to taste and toss gently to coat.
Using your hands, shape the quinoa into fritters about the size of a walnut (in shell) around a center made of avocado.
Working in batches, gently slide the fritters into the hot oil. Fry until golden brown, about 3 to 4 minutes, turning as necessary. Drain on paper towels and serve warm.