For the bÃ©arnaise sauce, bring the white wine vinegar, bay leaf, shallot, tarragon and parsley to the boil in a heavy-based non-reactive pan. Season, to taste, with salt and freshly ground black pepper. Continue to simmer until the volume of liquid has reduced by two thirds (there should only be one tablespoon of liquid remaining in the pan). Strain the remaining liquid immediately into a cold bowl.
In a heatproof bowl, mix together the egg yolks with a pinch of salt until well combined. Add one teaspoon of the reduced liquid and one cube of butter.
Suspend the heatproof bowl over a pan of simmering water (do not allow the base of the bowl to touch the surface of the water). Whisk the butter and reduced liquid into the egg yolk and salt mixture, whisking continuously, until well combined. Add the remaining cubes of butter, one at a time, whisking until each one has been incorporated into the mixture before adding the next.
When all of the butter has been incorporated into the mixture and the sauce is smooth, stir in the tarragon and parsley and season again, to taste. Set aside.
For the steak and chips, preheat the oven to 220C/425F/Gas 7. Brush each fillet steak all over with a little oil, then season, to taste, with salt and freshly ground black pepper.
Heat a frying pan over a medium heat until hot. Add the fillet steaks and fry for 1-2 minutes on each side.
Transfer the steaks to a baking tray and roast in the oven for a further 5-6 minutes (for medium rare) or longer for medium to well done. Remove from the oven and set aside to rest for 8-10 minutes.
Meanwhile, heat the oil in a deep fat fryer to 180C. lternatively, heat the oil in a deep heavy-based frying pan until a breadcrumb sizzles and turns brown when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.) Carefully lower the dried parboiled potato chips into the hot oil and fry for 6-8 minutes, or until crisp and golden-brown. Remove from the pan using a slotted spoon and set aside to drain on kitchen paper.
To serve, place one fillet steak onto each of four serving plates. Arrange some of the chips in a stack alongside. Drizzle the bÃ©arnaise sauce over the steak. Serve the salad leaves alongside.