Preheat the oven to 400°.
Bring steaks to room temperature for about 30 minutes.
Heat a large skillet.
Dry the filets with a paper towel.
Brush the filets lightly all over with the oil. Season both side wells with sea salt and pepper.
When the pan is hot, add the steaks and sear evenly on all sides for about 2 minutes per side or until well browned. If the steaks won’t release from the pan, wait another minute or so and it will release when browned.
Arrange the steaks on a parchment lined baking sheet and place into the oven and cook until 120°, about 10 minutes. Remove from oven and let rest for 5 minutes.
Asparagus and Crab
While the steaks are cooking you can lightly steam the asparagus or cook it in the still hot pan that you cooked the steaks in.
Cut the stems from the asparagus so the spears are all the same length. Lightly toss with a little olive oil and season with salt and pepper. Cook until you can pierce with a knife, about 5 minutes. Let rest until you’re ready to assemble the dish.
Warm the crab in a steamer basket over simmering water for about 5 minutes.
Make the bearnaise sauce at the very last minute.
Place the steaks on two plates, top with asparagus spears, then add the crab and drizzle with sauce.