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Preheat oven to 400 degrees F.
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Take the beef tenderloin and drizzle with olive oil.
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Season well all over with plenty of kosher salt and freshly ground black pepper all over.
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Make sure it is at room temperature before cooking.
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Place a large cast iron skillet over medium-high heat on the stove top and sear tenderloin all over.
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Place the whole pan in the oven and roast the tenderloin for 15-17 minutes (depending on how thick your tenderloin is).
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An instant-read thermometer when inserted into the thickest part of the meat should read 130 degrees F for medium-rare.
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If you want it medium, cook for a further 3 minutes in the oven.
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Remove from the oven and tent with foil while you let it rest for 10 minutes before cutting.
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Make the bearnaise reduction first.
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In a small saucepan, combine half of the tarragon, shallots, vinegar and wine over medium-high heat.
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Bring to a simmer and cook until reduced by half.
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Remove from heat and set aside to cool.
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Blend yolks and bearnaise reduction together in a blender.
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With the blender running, add 1/3 of the butter in a slow steady stream.
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Once it emulsifies, turn the blender speed up to high and add the remaining butter.
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Add the remaining half bunch of fresh tarragon leaves, season with salt and pepper and give it 1 more buzz.
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Set aside in a warm spot to hold the sauce.
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*RAW EGG WARNING
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Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness.
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To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.
