6 pieces arctic char fillet (1 to 1 1/4 inches thick) with skin (6 ounces each)
1/2 tablespoon vegetable oil
Directions
Coarsely chop pistachios in a food processor, then add basil, shallot, salt, pepper, and 6 tablespoons butter and purée until mixture forms a paste.
Preheat oven to 400°F.
Remove any bones from fish with tweezers and pat fish dry.
Heat oil and remaining 1/2 tablespoon butter in a 12-inch nonstick skillet over moderately high heat until foam subsides, then brown skin sides of fillets in 2 batches, 3 to 4 minutes per batch. Transfer fillets as browned, skin sides down, to a lightly oiled shallow baking pan (1 inch deep).
Divide pistachio paste among fillet pieces and spread evenly in a 1/8-inch-thick layer over top of each.
Bake fillets in middle of oven until just cooked through, 9 to 11 minutes.