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Rinse and pat dry the chicken thighs with paper towels. Using a knife or your fingers carefully separate the skin from the flesh, so that a pocket remains between the two.
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Rub salt and paprika all over the chicken, both into the flesh and the skin.
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Spread pesto evenly among the 4 chicken thighs, rubbing it under the skin, onto the flesh.
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Broil on high for 20 minutes (10 minutes on a lower oven shelf, and 10 minutes on a higher oven shelf to crisp up the skin). Cook for additional 5 minutes if needed, or until chicken is cooked through.
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To make the romesco sauce pulse almonds in food processor until they resemble fine crumbs. Add remaining ingredients, roasted red peppers, apple cider vinegar, garlic, olive, oil, tahini, smoked paprika and salt. Process until almost smooth.
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Serve chicken topped with a dollop of romesco sauce with sliced roasted red pepper and basil for garnish.