Preheat oven to 350°F. Butter 11 x 7 x 2-inch glass bakin dish. Bring milk to boil in medium saucepan. Remove from heat. Melt 4 tablespoons butter in heavy medium saucepan over low heat. Add flour; stir 3 minutes. Gradually whisk in warm milk. Increase heat to medium; whisk constantly until mixture is thick and smooth, about 4 minutes. Remove sauce from heat. Whisk in yolks. Cool slightly.
Melt 1 tablespoon butter in large skillet over medium heat. Add shallots; sauté until tender, about 3 minutes. Transfer to large bowl. Mix in sauce, spinach, 1 1/3 cups cheese, salt, pepper and nutmeg.
Using electric mixer, beat egg whites in large bowl until stiff but not dry. Fold whites into spinach mixture in 2 additions. Transfer to prepared baking dish. Sprinkle remaining 2/3 cup cheese over. Bake until puffed and set about 45 minutes.