Method
To prepare: Put 2 Tbsp of the sesame oil in a small mixing bowl; stir in the soy sauce, grated lime zest and lime juice. Season with salt and pepper; set aside.
Place the fish fillets on a cookie-type baking sheet and season with salt and pepper.
Put the egg white in a small mixing bowl; beat it with a fork until it is frothy, about 30 seconds. Pour the egg white over the fillets, turning them to coat both sides completely.
Put the remaining 2 tsp of sesame oil in a large, nonstick skillet set over medium heat. When the oil is hot, place the fillets in the pan, round side down. Brown the fillets, without moving them, until the egg has set, 2-4 minutes. Sauté the fillets 3-4 minutes more until the first side is golden.
Turn them over and cook the second side for 3-5 minutes, or until the fillets are just cooked through.
To serve, place the fillets on warm dinner plates, give the lime oil a stir, spoon some over each fillet and serve immediately.