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Heat a grill pan or grill to medium-high heat. Place scallions on a small sheet tray and drizzle two tablespoons olive oil and 1/2 teaspoon kosher salt. Grill for about 3-5 minutes per side, until starting to char and brown. Remove and allow to cool while you prepare the other ingredients.
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Add garlic cloves to a food processor and pulse until minced. Add grilled scallions, basil, and pine nuts and pulse until combined. With food processor running, drizzle in remaining 1/2 cup olive oil through the top. Pulse until creamy. Add lemon juice and season with salt and pepper to taste; pulse several more times to combine.
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Season lamb chops on all sides with olive oil, salt and pepper. Grill over medium-high heat for about 4 minutes per side. Allow to rest for 5-10 minutes before serving with scallion pesto and pine nuts..