To make the slaw, mix all ingredients, including lime zest and juice, soy sauce, sesame oil and seasonings.
To make the salsa, combine all prepared ingredients in a bowl and refrigerate to chill.
Cut fish into 4 to 6 ounce portions. Incise the snapper and season with salt and pepper. In a skillet on medium high heat, sear skin side down with olive oil and butter until crispy. While the skin is getting crispy, continuously baste the flesh side of the fish with the hot butter and oil. Once the skin is crispy, turn the fish over in the pan and remove from the heat. Let it rest in the hot pan for 2-3 minutes.
To serve, spoon slaw onto a serving plate and place the cooked fish on top. Top with the mango chili salsa and garnish with fresh green onion and cilantro.