Dust whiting in flour and shake to remove excess. Dip in egg, then coat in crumbs.
For gribiche sauce, process boiled and raw egg yolks in a food processor with mustard and vinegar until combined, then with motor running add oil in a thin steady stream until combined. Season to taste with sea salt and freshly ground white pepper. Finely chop eggwhite, add to sauce with remaining ingredients and stir to combine.
Heat oil in a large saucepan to 180C, fry whiting, for 4-5 minutes or until golden, then drain on an absorbent paper-lined plate.
Spread rolls with butter, top with watercress, 2 whiting fillets, gribiche sauce, sandwich and serve immediately.