Preheat oven to 400°.
Add quinoa and 2 cups water or chicken broth to medium sauce pan. Bring to a boil. Cover and reduce heat to simmer. Simmer for 20 mins. Remove from heat.
Meanwhile, cook broccoli in microwave according to package directions, reducing cook time to 2 1/2 minutes.
Meanwhile, heat a Dutch oven over medium-high heat. Coat pan with cooking spray. Add chicken to pan; sprinkle with salt & pepper. Cover and cook 5 minutes or until browned, turning occasionally; remove from pan.
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.
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