Heat oven to 425°F. Grease casserole dish.
Heat butter in saucepan over low heat until melted. Stir in baking mix, salt, & pepper until blended. Stir in milk & broth. Heat to boiling, stirring. Boil & stir 1 minute. Stir in chicken, cheese, & Green beans. Pour evenly into casserole dish.
Beat egg whites until soft peaks form. Set aside.
Beat egg yolks until thick.
Mix baking mix, salt, & paprika. Beat into yolks alternately with milk & oil. Fold in egg whites. Spread topping over filling in baking dish.
Bake until golden, 20 minutes. Let stand 5 minutes.