Step 1: Season the steaks generously with salt and pepper and let them sit at room temperature for at least 30 minutes before cooking.
Step 2: In a small saucepan over medium heat, combine the vinegar, minced shallot, and half of the tarragon. Simmer until the liquid is reduced to about 1 tablespoon, then remove from heat and let cool slightly.
Step 3: To make the Béarnaise, whisk the egg yolks into the vinegar reduction. Place the bowl over a pot of simmering water (double boiler) and slowly drizzle in the warm melted butter while whisking constantly until the sauce thickens and emulsifies.
Step 4: Stir in the remaining tarragon and lemon juice; keep the sauce in a warm spot (not hot) until ready to serve.
Step 5: Heat a cast-iron skillet over medium-high heat with olive oil and butter. Once smoking slightly, add the steaks and sear for 3-4 minutes per side for medium-rare. Remove and let rest for 5-10 minutes.
Step 6: While the steaks rest, blanch the asparagus in boiling water for 2-3 minutes until tender-crisp, then drain.
Step 7: In the same skillet used for the steaks, gently warm the crab meat with a tablespoon of butter and a squeeze of lemon juice for 1-2 minutes.
Step 8: To assemble, place the steaks on plates, top each with 4-5 asparagus spears, a generous portion of crab meat, and a heavy drizzle of Béarnaise sauce.