Preheat oven to 425°F.
Whisk together turmeric and 2 tablespoons oil; season with salt and pepper.
Season fish with salt; coat in turmeric mixture.
Heat 2 tablespoons oil in a large nonstick skillet over medium-high.
Add fish, skin-sides down; cook, undisturbed, until crisp, 4 minutes.
Transfer to a parchment-lined baking sheet, skin-sides up; roast until cooked through, 6 to 8 minutes.
Wipe skillet clean; heat over medium.
Add remaining 1 tablespoon oil, ginger, and shallot; cook, stirring, until fragrant.
Stir in greens and cook, tossing, until just wilted, 1 minute.
Add coconut milk, ¾ cup water, and chickpeas.
Season and cook, stirring occasionally, until slightly reduced, 5 minutes.
Stir in lime zest and juice.
Serve over rice, with fish, cilantro, coconut, and lime wedges.
