Place and core apples and slice paper-thin (the thickness of apples is important as they barely cook). Add the rum or lemon juice and sugar. Mix well and let stand until ready to use.
Beat eggs with the sugar and cold water, then add the apple mixture. Cook according to directions fold and serve.
To flame the omelet sprinkle top with 2 tablespoons of sugar and pour 3-4 tablespoons of hot rum over it. Set the rum afire and keep pouring it over the flaming omelet until the fire dies out.
