How to Make It
Pour a little vinegar over the fish fillets, then rinse them under cold, running water. Pat the fillets dry with paper towels and arrange them on an ovenproof glass or ceramic platter. Rub a little salt over the skinless sides of the fillets and sprinkle with the lemon juice. Spread half of the bread crumbs over the fillets and drizzle them with 1 tablespoon of the olive oil; turn the fillets and repeat with the remaining bread crumbs and olive oil. Cover and let marinate at room temperature for 30 minutes.
In a mini food processor, combine the thyme leaves, lemon juice, mustard and salt. Pulse for 1 minute. Add the butter and process until completely smooth. With the machine on, add the olive oil in a thin, constant stream until fully incorporated. Season the sauce with salt and pour into a sauceboat.
Preheat the oven to 400° or light a grill. Bake the fish on the platter until just cooked through, about 12 to 15 minutes. Alternatively, grill the fish, skin side down for skin-on fillets, for about 5 minutes; turn the fillets and grill just until they flake, about 4 minutes longer. Transfer the fish to a platter. Pour the salmoriglio sauce over the fish fillets and serve.