Preheat oven to 475°. Meanwhile, in a small frying pan, combine 1/2 tsp. coriander and the cumin, turmeric, cayenne, and cardamom. Toast over medium heat, stirring, until fragrant and just a bit darker, about 2 minutes. Pour into a bowl and stir in 2 tbsp. each oil and cilantro, the green onion, lemon juice, chile, and 1/4 tsp. salt. Stir in fruit and set aside.
In center of a rimmed baking sheet, combine remaining 1 1/2 tsp. coriander, 1 tbsp. oil, and 1 tsp. salt. Turn fish in paste to coat (if fish has skin, arrange it skin side down). Bake fish until no longer translucent in center (cut to test), 8 to 12 minutes for sablefish, about 5 minutes for sole.
Transfer fish to plates and spoon salsa on top. Sprinkle with remaining cilantro.