For the salsa: Combine all ingredients together in a mixing bowl. Make up to a day in advance. Keep covered in the refrigerator.
For the shrimp: In a mixing bowl, combine jalapenos, garlic, ginger, brown sugar, soy sauce, lime zest, coconut milk, basil, vegetable oil, salt and pepper. Add the shrimp and marinate for at least 30 minutes and up to 4 hours, refridgerated.
Heat a nonstick skillet over high heat. Use tongs or a fork to remove the shrimp from the marinade and place in an even layer in the pan, reserving the marinade.
Cook the shrimp until well browned on each side, turning once, about 3 to 4 minutes total. Transfer cooked shrimp to a serving plate.
Add reserved marinade to pan, bring to a boil and cook until slightly thickened, about 5 minutes.
Pour over the cooked shrimp and serve with Lime Jasmine Rice and Mango Salsa.
Put the rice, coconut milk, water, and salt in a saucepan and bring to a simmer. Cover and gently simmer until liquid is absorbed, about 12 to 15 minutes. Fluff with a fork and stir in the lime zest. Serve immediately.