How to Make It
Make the corn puree In a medium saucepan, melt 2 tablespoons of the butter. Add the corn and cook over moderate heat, stirring occasionally, for 5 minutes. Add the cream and bring to a simmer. Cook over moderately low heat, stirring occasionally, until reduced by half, about 15 minutes. Transfer to a blender, add the remaining 2 tablespoons of butter and puree until smooth. Season with salt and keep warm.
Make the lemon-butter sauce In a small saucepan, bring the lemon juice to a simmer over low heat. Add the butter a few cubes at a time, whisking constantly and waiting until the butter has melted before adding more. Season the sauce with salt and keep warm.
Make the snapper In a large nonstick skillet, heat 2 teaspoons of the oil. Add the corn and cook over moderately high heat, stirring occasionally, until charred, 3 to 4 minutes. Transfer the corn to a paper towel-lined plate; wipe out the skillet.
Heat 1 tablespoon of the oil in the skillet. Rub the snapper fillets with the remaining 1 tablespoon of oil and season with salt and pepper. Add the fish to the skillet skin side down and cook over moderate heat until the skin is golden brown, about 4 minutes. Flip the fillets and cook until just white throughout, 2 to 3 minutes longer.
Spoon the corn puree into shallow bowls and top with the snapper. Drizzle with the lemon-butter sauce, garnish with the charred corn and chopped chives and serve.