Crack the eggs into a suitable bowl, season with a pinch of salt, add 3 tbsp of whipping cream and mix.
Put the sugar in a saucepan with 2 tbsp of water and let it melt while stirring. When the sugar solution starts to brown, add the walnuts and stir to brown. Then add 1 tbsp water and the remaining whipping cream. While stirring continuously, also cook the whipped cream until creamy. Then remove the saucepan from the stove.
In a hot frying pan with a little butter, add the beaten egg. Stir with a wooden spoon until only a little liquid egg remains. Remove the frying pan from the stove and shake it so that the omelet takes on a cylindrical shape.
With a kitchen knife, make a long cut in the center of the top of the omelet and fill it with the caramelized walnuts.
Divide the filled omelet and serve.