How to Make It
In a large nonstick skillet, heat 2 tablespoons of the olive oil until shimmering. Season the rockfish with salt and pepper and add it to the skillet skin side down. Cook over moderately high heat, pressing gently with a spatula, until the skin is browned and crisp, about 3 minutes. Flip the fillets and cook until flaky and white throughout, 3 to 4 minutes longer; transfer to a plate and keep warm.
Meanwhile, in a medium saucepan, heat the remaining 1 tablespoon of olive oil until shimmering. Add the shallot and cook over moderate heat, stirring, until just softened, about 1 minute. Add the wine and simmer until nearly evaporated, about 3 minutes. Reduce the heat to moderately low, add the heavy cream and simmer until thickened, about 3 minutes. Add the oysters with their liquor and bring just to a boil. Simmer over moderately low heat until the oysters are just cooked, about 2 minutes. Stir in the 1 tablespoon each of chives and tarragon and season the sauce with salt and pepper.
Transfer the rockfish to shallow bowls and spoon the oyster sauce on top. Garnish with chives and tarragon and serve right away with braised kale.