Take the steak out of the refrigerator and bring to room temperature. Pat the steak dry. Coat the steak well with the coffee mixture and rub it in.
Add shallots, tarragon, black peppercorns, white wine vinegar and white wine to a preheated pan. Reduce the liquid down to about 2 tablespoons. Pass through a fine mesh strainer, squeezing the liquid from the mixture.
Heat a cast iron pan over high heat. Flip the steak every minute, forming a nice sear. The steak should feel springy to touch, so as not to overcook it. Add butter and baste the steak. Rest for 5-8 minutes, about half the cooking time, before slicing and serving.
Fill a pot with an inch of water and bring it to a simmer. Add egg yolks to a large stainless steel bowl and place over the pot. Add reduced tarragon, shallot, and black pepper liquid to the bowl. Whisk quickly, taking it on and off the heat and adding butter, to ensure the eggs do not cook. Once it foams up, add butter one cube at a time. Season when the sauce thickens doubles in volume.
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