Preheat oven to 400 degrees F.
To a large skillet, add 1 Tbsp olive oil and heat over MED heat. Add chopped onion, carrot and chicken sausage and saute 5-7 minutes, until vegetables are softened and sausage is lightly browned. Remove to a large mixing bowl, reserving the pan drippings in the skillet.
While onions, carrots and sausage are sauteing, add broccoli florets to a large microwaveable bowl with a splash of water. Cover bowl with a plate and microwave on high for 4-5 minutes, to steam. Drain broccoli and add to the large mixing bowl.
Add butter and garlic to pan drippings, melt. Add flour and whisk until mixture is combined and no flour lumps remain.
Add milk and chicken stock, whisking to remove any lumps from the flour/butter mixture. Bring to a high simmer and cook, whisking often for 2-4 minutes. Mixture will thicken quite a bit.
Add thyme, salt, pepper, and red pepper flakes, stirring to combine. Add in 1 cup shredded cheddar cheese, whisking to melt cheese into sauce.
Add cooked quinoa to large mixing bowl with other cooked ingredients. Pour in cheese sauce and stir to combine well.
Spray a 3 qt. casserole dish (13x9") with non-stick cooking spray and transfer 1/2 the mixture to dish. Sprinkle with 1/2 cup cheddar cheese, the top with remaining half of mixture.
Toss panko breadcrumbs with remaining 1/2 Tbsp olive oil, and sprinkle over top of casserole. Top with 2/3 cup cheddar cheese and 1/3 cup mozzarella cheese.
Bake for 18-20 minutes, until lightly browned and bubbly.