Whisk the eggs together, adding salt and pepper, and chill.
To make the watercress sauce, put the white wine in a thick-bottomed pan and reduce buy half. Once reduced add fish stock and reduce by half again. Add double cream, bring to the boil slowly, add watercress and simmer for 10 minutes approximately.
Remove sauce from heat and liquidise; pass through a sieve and return to a very low heat until ready for omelettes.
Heat omelette pan and when very warm, add 1 tablespoon of olive oil. Swirl around and add enough omelette mix for one. Keep moving mix around with fork and when starting to cook, spread over bottom of pan and add a quarter of smoked salmon. Fold omelette over and place on plate. Cover with watercress sauce and serve. Repeat for each omelette.