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Combine basil, olive oil, Parmesan cheese, garlic, and pine nuts in a food processor and puree until smooth. Season with salt and pepper.
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Preheat the oven to 200 degrees F (95 degrees C).
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Rub salt over steaks. Spread some pesto evenly on both steaks and place into an oven-safe glass dish. Pour oil into the dish, ensuring there is enough oil to submerge the steaks.
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Cook steaks in the preheated oven for 40 minutes. An instant-read thermometer inserted into the center should read 135 degrees F (57 degrees C). Drain steaks and blot off excess oil.
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Heat a cast iron or nonstick skillet over medium-high heat. Sear steaks in the hot oil on both sides and the edges for 30 to 45 seconds.
Editor's Note:
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