Preheat the oven to 375 degrees F (190 degrees C). Spray a casserole dish with cooking spray.

Combine vegetable broth, garlic, salt, and pepper in a pot over medium-high heat and bring to a boil. Add quinoa, cover, reduce heat, and simmer until tender, about 15 minutes. Let stand 5 minutes.

Heat olive oil in a skillet over medium-low heat. Add spinach, carrots, and red peppers and cook until barely tender, about 5 minutes.

Mix chicken, cooked quinoa, cooked vegetables, Alfredo sauce, and basil together in a bowl. Pour into the prepared casserole dish, patting it down with a spoon.

Melt butter in a small saucepan over medium heat and mix in bread crumbs until evenly coated. Remove from heat and stir in Parmesan cheese. Evenly distribute cheese crumbs over the top of the casserole.

Bake in the preheated oven until cooked through and lightly browned on top, 25 to 30 minutes.