1. Combine 1 cup water, 1 tablespoon salt, and sugar in a shallow dish. Add fillets, and let stand 15 minutes. Remove fillets from brine; pat dry. Discard brine. Brush fillets with 1 tablespoon olive oil. Sprinkle with 1/2 teaspoon salt and pepper.
2. Preheat broiler.
3. Place fillets on a broiler pan coated with cooking spray; broil 7 minutes or until desired degree of doneness.
4. Combine arugula, frisée, and mint in a large bowl. Combine apple and 1 tablespoon oil; toss well. Add apple and 1/4 teaspoon salt to arugula mixture, and toss gently.
5. Combine remaining 1 tablespoon oil, remaining 1/4 teaspoon salt, parsley, and remaining ingredients, stirring with a whisk until blended. Divide arugula mixture evenly among 6 plates; top each serving with 1 fillet. Drizzle about 1 tablespoon sour cream mixture over each serving.