Heat 14g of butter and sauté shallots, garlic, thyme, bay leaf, and peppercorns for 3 minutes until soft.
Add white wine and vinegar, boil until mostly evaporated, then whisk in chilled butter cubes until glossy.
Strain sauce through a sieve, season with salt and lemon juice, and keep warm.
Heat a frying pan and season flour with salt and pepper.
Dredge trout fillets skin-side down in flour and dip the floured side in sunflower oil.
Fry trout floured-side down for 4 minutes until skin is crisp and golden.
Turn trout over and fry for 1 more minute until cooked through.
Boil samphire for 3 minutes, drain, then toss with butter, lemon juice, and pepper.
Plate samphire, top with trout, and finish with beurre blanc sauce.