Preheat oven to 350°F. Butter 11 x 7 x 2-inch glass baking 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. (Can be made 2 hours ahead. Cover and let stand at room temperature. Stir over low heat until just lukewarm before continuing.)
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
