In a small saucepan, combine quinoa and water then bring to a boil over high heat. When it boils, turn down the heat to low and simmer for about 15 minutes or until the water is completely absorbed. Let it cool.
In a large bowl, add the chickpeas and mash with a fork or potato masher. Add the cooled quinoa, egg, bread crumbs, Parmesan cheese, onion, 2 tablespoons parsley, 1/2 teaspoon oregano, 1/2 teaspoon salt, and pepper. Mix well. If it needs to be more compact, add additional bread crumbs.
Shape 10 mini burger patties, cover then refrigerate for about 2 hours.
While the burgers are in the refrigerator, grill the vegetables on a griddle. When the vegetables are tender, place them in a medium bowl and mix in 1 tablespoon extra virgin olive oil, balsamic vinegar, the remaining oregano, parsley, salt and pepper. Set aside.
Over medium heat, in a large nonstick skillet or griddle, add with the remaining extra-virgin olive oil, cook the patties until heated through and crisp.
Over medium heat, on the same (clean) griddle or skillet where you cooked the vegetables, lightly brown the inside of the buns.
When all the ingredients are ready, place lettuce on the buns, the burgers, and the grilled vegetables.