Preheat the oven to 450°F. Bring the steaks to room temperature (preferred but not required), pat them dry, and season with salt and pepper.
Heat the olive oil in a cast iron, or other oven-proof skillet, over high heat. Sear the steaks for 2 to 3 minutes on each side until browned. Slide the skillet into the hot oven and cook until desired doneness is reached (times vary depending on thickness). See notes for cooking times.
Remove from oven, slip an oven mitt over the handle, and let rest for a few minutes before topping with bearnaise sauce (below) and serving.
For the Blender Béarnaise Sauce
Place the egg yolks in the bottom of a handheld blender cup (preferred) or countertop blender, pulse a few times, and set aside. (NOTE: My handheld blender works with a pint-sized wide-mouthed glass mason jar for this recipe.)
In a small saucepan combine the vinegar, water, shallots, and tarragon and bring to a light boil for 2 to 3 minutes until the liquid reduces by half and the shallots soften. With the blender on, slowly pour in the warm vinegar mixture and blend until well combined.
In the same saucepan, melt the butter and bring it to a light boil. With the blender on, slowly pour in the hot butter and blend/pulse until sauce reaches the desired thickness (similar to a gravy). Season with salt and pepper, pour over top of the steaks, and serve.
Cooking Times for 1 1/2" Thick Steaks:
9 to 11 minutes for Medium Rare (RED / 130 - 140°F)
11 to 14 minutes for Medium (PINK / 140-150°F)
14 to 18 minutes for Medium Well (BROWN / 150-160°F)
They can cook very quickly at the end and even a little after taken out of the oven, so it's always better to take them out a little early!