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 (addone minute per side for medium).
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.
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.
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.
Reduce heat to medium and add capers. Stir to combine and cook for another minute or until heated through.
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!