Preheat oven to and spray an 8-inch-square baking dish with non-stick cooking spray.
Heat oil in a medium skillet over medium heat until hot. Add onion and garlic and sauté for 1 minute or until onion is tender. Add quinoa and cook, stirring, until golden brown and toasted, 2 to 3 minutes. Add 2 1/2 cups water, bring to a boil, reduce heat to medium-low and simmer, covered, until water has been absorbed, about 10 minutes. Remove from heat.
Whisk eggs and milk together in a large bowl. Stir quinoa into egg mixture, and whisk in 1/2 cup of the cheese. Spread in the prepared baking dish and sprinkle with remaining 1/2 cup cheese. Bake for 30 minutes. Garnish with chopped tomato and green onion, if desired. Serve immediately.