Preheat oven to 350 degrees. Lightly spray a 9x9 baking dish with nonstick cooking spray.
In a saucepan, heat water to boiling. Add quinoa and return to a boil. Reduce heat and simmer, covered for 15 minutes. Remove from heat.
Meanwhile, heat oil over mediumhigh heat. Season chicken pieces with salt and pepper. Add to pan and cook for 5 minutes. Remove from pan.
Heat butter in pan, stirring to remove any bits from the bottom. Stir in flour and cook for 1 minute. Gradually add milk letting each addition fully incorporate prior to adding more. Bring to a boil and then reduce heat to simmer. Simmer for 5 minutes. Remove from heat and stir in 1 cup Swiss cheese and 1⁄2 cup Parmesan cheese.
Combine chicken, quinoa, artichokes, 2 Tbsp brine from artichokes, 1⁄4 cup Swiss cheese and cheese sauce in casserole dish. Stir to combine. Top with remaining Swiss and Parmesan cheese. Bake for 15 minutes.
Recipe by About a Mom at https://www.aboutamom.com/chicken-artichoke-quinoa-casserole/