Bring a large pot of water to a boil. Preheat oven to 375° F.
Béchamel Sauce: Heat milk until hot in a small saucepan. In a separate small saucepan, melt butter. Stir in flour with a wire whisk and cook over low heat for 2 minutes.
Add hot milk gradually to butter and flour mixture, mixing with a wire whisk until smooth and thickened. ADD beaten egg, 2/3 of the cheese, salt, and pepper. Mix until cheese is melted; set aside.
Heat olive oil in a large skillet over medium heat. Add onions and spinach. Sauté 2 minutes or until spinach is wilted. Add spinach to béchamel sauce and set aside.
Cook Elbows for 4 minutes. Drain and add to béchamel sauce; mix well.
Pour into a 13 x 9 inch glass baking dish; sprinkle with remaining cheese and bake for 25 minutes. Let rest 5 minutes before serving.
