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Heat two tablespoons olive oil in a large skillet over medium-high heat. Add tuna steaks to hot skillet and cook for approximately 2 minutes for rare (add one minute per side for medium).
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Flip tuna and season with salt and black pepper, to taste. Cook for another 2-3 minute, depending on desired level of doneness. Transfer tuna steaks to a plate and season with additional salt and black pepper, if desired. Keep warm.
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Add remaining olive oil and chopped shallots to skillet, Sauté, stirring occasionally, until shallots are soft and start to turn golden brown, approximately 3 minutes.
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Add white wine, chicken broth, lemon juice, and lemon slices to skillet. Deglaze pan by scraping up any brown bits from the bottom with a spatula. Cook, stirring frequently, until the liquid is reduced by half.
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Reduce heat to medium and add capers. Stir to combine and cook for another minute or until heated through.
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Transfer the tuna steaks onto individual serving plates and top with a “melted” lemon slice and a spoonful of the lemon-caper sauce and serve immediately with your favorite sides. Enjoy!