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Place the peppers directly on the burner of a gas stove over high heat or on a grill. Just as each section turns puffy and black, turn the pepper with tongs to prevent overcooking. (If you don't have a gas stove, place the peppers on a baking pan, and broil in the oven, turning as each side becomes charred.) Transfer the peppers to a large bowl, and cover immediately with plastic wrap. Let the peppers sweat until they are cool enough to handle, about 15 minutes. Transfer the peppers to a work surface. Peel off the blackened skin, and discard. Cut peppers in half and remove seeds.
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Add peppers to the jar of a blender along with avocado, 1/4 cup olive oil, 1/4 cup chopped onion, 1/4 cup cilantro leaves, lime juice, 1/4 teaspoon salt, and 3 tablespoons water. Blend until smooth; set aside.
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Preheat a grill pan over medium heat. Season halibut with remaining salt and pepper. Rub both sides of fish with remaining 3 tablespoons olive oil and transfer to grill pan. Cook, turning once, until cooked through, about 4 minutes per side. Remove from grill and cut into small pieces.
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Divide fish evenly among the tortillas. Place 1 tablespoon chopped onion and 1 tablespoon cilantro leaves over fish. Top each with a piece of tomato. Add salsa and squeeze over lime halves; serve immediately.
