In food processor container, place salmon, egg, bread crumbs, garlic, soy sauce, basil, and lime zest, and pulse several times until you have a chunky mixture. Form into 4 patties.
In large bowl, whisk together lime juice, fish sauce, sesame oil, and sugar. Stir in tomatoes, mango, green onions, chili pepper, and cilantro.
In large skillet over medium-high, heat oil. Place salmon burgers in skillet and cook for 3 minutes on each side, or until crispy on the outside but just barely cooked through in middle, to an internal temperature of 145 F (63 C). Alternatively, you can prepare the burgers on an outdoor grill over medium heat, making sure grill grates are well greased.