Preheat grill to high (450°F to 550°F). Toss tomatillos with 1 tablespoon of the oil and 1/2 teaspoon each of the salt and pepper. Grill, uncovered, turning occasionally, until blistered and charred, about 7 minutes. Cool 5 minutes.
Process grilled tomatillos, avocado, lime juice, garlic, and remaining 3 tablespoons oil, 1 teaspoon salt, and 1/4 teaspoon pepper in a food processor until smooth, 2 to 3 minutes.
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