1. Heat a medium saucepan over medium-high heat. Add 1 1/2 teaspoons oil; swirl to coat. Add quinoa; cook 2 minutes or until toasted, stirring frequently. Add 1 1/4 cups water; bring to a boil. Cover, reduce heat, and simmer 15 minutes or until quinoa is tender. Remove from heat; let stand 5 minutes. Fluff with a fork.
2. Preheat oven to 400°.
3. Cook broccoli in microwave according to package directions, reducing cook time to 2 1/2 minutes.
4. Heat a Dutch oven over medium-high heat. Coat pan with cooking spray. Add chicken to pan; sprinkle with 1/8 teaspoon salt and 1/8 teaspoon pepper. Cook 5 minutes or until browned, turning occasionally; remove from pan.
5. Add remaining 1 tablespoon oil to pan; swirl to coat. Add onion and garlic; sauté 5 minutes. Combine milk and flour, stirring with a whisk. Add milk mixture, stock, remaining 3/8 teaspoon salt, and remaining 3/8 teaspoon pepper to pan. Bring to a boil, stirring frequently; cook 2 minutes or until thickened. Remove from heat; cool slightly. Add Parmesan, stirring until cheese melts. Stir in quinoa, broccoli, chicken, and mayonnaise. Spoon mixture into a 2-quart glass or ceramic baking dish coated with cooking spray. Sprinkle with cheddar. Bake at 400° for 15 minutes or until casserole is bubbly and cheese melts.