Sift flour into a large bowl. In another large bowl, whisk egg yolks. Mix in beer, butter and salt. Set aside 1 cup of flour for dipping the onion rings. Slowly stir the egg yolk mixture into the remaining flour and mix well. Allow the mixture to stand 30 to 60 minutes.
Heat deep fryer to 375 degrees F (190 degrees C).
In a small bowl, stiffly beat the egg whites. Gently combine the egg whites with the batter.
Coat each onion ring with flour and dip into batter.
Deep fry the battered rings, several at a time, until golden brown. Drain on paper towels and serve.