Break the eggs into a basin, add the sugar, cream, and vanilla, and beat them till they are lightly mixed together. Heat the butter in an omelet pan, pour in the egg mixture, and stir it over a quick fire till it begins to thicken and set.
Meanwhile, put the jam into a small pan on the fire, and heat it gently. As soon as the mixture begins to set, spread the jam lightly over it, and quickly fold over first one side of the omelet, and then the other, so as to quite hide the jam. Hold the pan for a minute or two in front of a hot fire, then gently slip the omelet out on to a hot dish, and serve it as quickly as possible.