Melt a tiny bit of butter in a small saucepan over medium heat. Add the shallots and a pinch of salt and pepper and stir to coat. Stir in vinegar, reduce heat to medium-low, and cook until vinegar is evaporated, about 2-3 minutes. Reduce heat to low and continue cooking shallots, stirring frequently, until tender and translucent, about 3 minutes longer. Transfer shallot reduction to a small bowl and let cool completely.

Meanwhile, fill a blender with hot water to warm it and set aside. Melt 1/2 cup butter in a small saucepan over medium heat until butter is foamy. Transfer butter to a measuring cup.

Drain blender and dry well. Combine egg yolk, lemon juice, and 2 tsp. water in warm, dry blender. Purée mixture until smooth. Remove lid insert. With blender running, slowly pour in hot butter in a thin stream of droplets, discarding milk solids at bottom of measuring cup. Continue blending until a smooth, creamy sauce forms, 2-3 minutes. Pour sauce into a medium bowl. Stir in shallot reduction and tarragon and season to taste with salt, pepper, and more lemon juice, if desired. DO AHEAD: Can be made 1 hour ahead. Cover and let stand at room temperature.

Preheat oven to 275° F. Place a cooking rack on top of a foil lined baking sheet and set aside.

Dry meat with a paper towel and top with salt and pepper. Insert an oven-safe thermometer in to the thickest part of the meat.

When oven is preheated, place meat on top of cooling rack and place in oven. Roast until thermometer registers a temperature of 125-128° F. for medium-rare or 135-138° F. for medium.

Remove from oven and allow to rest while you preheat your skillet.

Heat a skillet (I love cast iron!) over medium-high heat. Add 1 Tbsp. olive oil and 1 Tbsp. butter to pan. Once heated, add the beef and sear on all sides. Remove to a cutting board to rest for another 5 minutes. Slice and serve topped with Bernaise sauce.