Place egg yolks and cream in a bowl and whisk until foamy, then season to taste. Using an electric mixer, whisk eggwhites until peaks form, then gently fold into egg yolk mixture.
Heat a quarter of the butter in an 18cm non-stick frying pan, add a quarter of the egg mixture and cook for 3 minutes or until base and edges are set, then scatter with a quarter of the goats cheese and sorrel. Fold in half and cook at 180C for 3 minutes or until puffed. Repeat 3 more times with remaining egg mixture, cheese and sorrel.
Meanwhile, heat olive oil in a frying pan and cook chorizo over medium heat, turning occasionally for 5 minutes or until browned. Serve omelettes with chorizo and relish.