1. In a large bowl, whisk the lime zest and lime juice with the rice vinegar, brown sugar and soy sauce. Whisk in the 1/4 cup of vegetable oil and season with salt and pepper. Add the sliced green mango, cucumber, cilantro, mint and 1 tablespoon of the roasted sesame seeds.
2. Light a grill or preheat a grill pan. Brush the salmon fillets with vegetable oil and season them with salt and pepper. Grill the salmon skin side down over moderate heat, turning once, until the skin is very crisp and the fish is slightly opaque in the center, 10 to 12 minutes. Transfer the salmon fillets to plates, sprinkle them with the remaining 1 tablespoon of roasted sesame seeds and serve with the mango salad.
MAKE AHEAD The green mango salad can be covered with plastic wrap and refrigerated for up to 4 hours. Add the chopped cilantro and mint just before serving.