Heat oven to 350 F. Line a 10x15-inch baking sheet with parchment paper or foil.
In a medium saucepan stir together quinoa and water. Bring to a boil over medium-high heat, stir once, reduce heat to low. Cover and cook 20 to 25 minutes or until the liquid is absorbed. Remove from heat and let rest for 5 minutes; fluff quinoa with a fork.
In a large bowl, stir together the cooked quinoa, tomatoes, red pepper, red onion, olives, 1 cup of the cheeze, parsley and green onions.
In a small bowl, mix together olive oil, lemon zest, lemon juice, salt and pepper. Pour over quinoa mixture, and toss to coat.
Spoon quinoa mixture into a mound on each avocado half. Top stuffed avocados with remaining 1/4 cup cheeze.
Place avocado halves on the prepared baking sheet. Bake 12 to 15 minutes or until cheeze is melted and the avocados are heated through. Garnish with additional parsley, lemon zest, salt and pepper, if desired.