Whisk together the egg yolks and cream, season. Beat the egg whites with the salt until stiff, carefully fold into the egg yolk mixture.
Heat the oil in a non-stick frying pan. Place half of the asparagus in the pan, fry for approx. 1 min. Pour half of the egg mixture over the asparagus. Cover the omelette and cook over a medium heat for approx. 5 mins. Top with half of the cheese and half of the basil, fold in the middle. Repeat these steps with the remaining ingredients.