Preheat oven to 375°F.

Cook rice according to package directions.

Heat half the oil in a large skillet over medium heat. Add onions and Cook until soft, 5 to 6 minutes. Add mushrooms and Cook an additional 5 to 6 minutes. Add garlic and Cook an additional minute. Remove from heat and Stir in spinach and parsley.

In a medium saucepan, Stir together flour and remaining oil and whisk in milk, simmering over medium heat, until thickened. Stir in cheese, nutmeg, salt, and pepper until smooth. Add the chicken.

Pour everything into a large casserole and fold together lightly until blended. Cover and bake 45 to 50 minutes until bubbly.