For the beurre blanc, heat one tablespoon of the butter in a non-reactive pan over a medium heat. When the butter has melted, add the shallots, garlic, thyme, bay leaf and peppercorns and fry for 2-3 minutes, or until the shallots have softened but not coloured.
Add the white wine and wine vinegar and bring the mixture to the boil. Continue to boil until most of the liquid has evaporated, then gradually whisk in the chilled butter cubes, one at a time, until all of the butter has been incorporated into the mixture and the sauce has thickened and is glossy.
Strain the beurre blanc through a fine sieve into a warmed bowl, then season, to taste, with salt and pour over the lemon juice. Keep warm. (NB: Do not leave the beurre blanc in too warm a place or the sauce may split.)
For the trout, heat a large frying pan over a high heat. Sprinkle the flour onto a plate and season, to taste, with salt and freshly ground black pepper. Pat the fish fillets fry with kitchen paper.
Dredge the trout fillets, skin-sides down, in the seasoned flour, then shake off any excess flour. Dip the floured sides of the trout fillets in the sunflower oil.
When the pan is hot, add the trout fillets, floured-sides down, and fry for 3-4 minutes, or until more than half of the trout flesh has turned opaque and the skin is crisp and golden-brown. (NB: The skin needs to be flat against the pan to crisp up all over, so press the trout fillets down with a fish slice if the heat makes them arch up.)
Turn the trout fillets over carefully and continue to fry for a further minute, or until the trout fillets are almost cooked through but are still slightly rare in the centre.
Meanwhile, for the samphire, add the samphire to a pan of boiling water (do not add salt) and cook for 2-3 minutes, or until tender. Drain well, then return the samphire to the pan, add the butter and lemon juice and season, to taste, with freshly ground black pepper.
To serve, divide the samphire between two warmed plates. Place the trout on top and spoon over the beurre blanc.