Prepare an large bowl of ice water. Set aside.

Bring a small pot of salted water to boil.

Add asparagus tips. Cook 60 - 90 seconds, just until the asparagus tips turn bright green.

Remove and immediately place in ice water to stop cooking.

Drain.

In a medium bowl, combine asparagus tips and crab meat. Toss gently to mix.

Preheat oven to 375°F.

Pat the steaks dry. Season both sides liberally with sea salt and cracked black pepper. Set aside.

Place butter and olive oil in a large oven-safe pan.

Place pan over medium high heat. Melt butter.

When butter and olive oil are hot and shimmering, place prepared steaks in the pan. Sear 3 - 4 minutes. Flip, sear for 3 minutes more.

Carefully place the pan into the oven. Cook steaks to an internal temperature of 135 degrees - medium rare (See chart in box below for other cooking times and temperatures).

Remove from oven.

Tent pan with foil to stay hot while you finish the sauce.

In a small heavy saucepan, add wine, vinegar, shallots and fresh tarragon.

Place saucepan over medium high heat and heat until boiling. Reduce heat slightly and continue to simmer gently until liquid is reduced to 2 tablespoons.

Strain liquid through a fine mesh sieve set into a medium bowl, pressing on and then discarding solids.

Whisk the yolks into the vinegar mixture.

Set bowl over a double boiler. Cook until hot, whisking constantly until yolks have thickened slightly.

Whisk in butter 1 piece at a time, adding each piece before previous one has melted completely.

Remove from heat. Whisk in lemon juice, 1/2 teaspoon salt, and 1/2 teaspoon pepper, to taste.

Keep warm until ready to use. (Leave on the double boiler but make sure to turn off the heat.)

Add about 1/3 cup of prepared warm Bearnaise Sauce to the bowl of crab and asparagus. Lightly toss to coat.

Place prepared steaks on serving plates.

Top with a generous portion of the crab-asparagus mixture.

Serve hot.