Step 1: Prepare Asparagus. Snap off woody ends. Blanch in boiling salted water for 2-3 minutes until tender-crisp. Transfer to an ice bath, then drain and set aside.
Step 2: Prepare Crab Meat. Gently pick through crab meat for shells. Place in a small bowl, drizzle with 1 tsp melted butter, and season with salt and pepper. Gently toss and set aside.
Step 3: Season Steaks. Pat steaks completely dry. Season generously on all sides with kosher salt and black pepper.
Step 4: Sear Steaks. Heat a heavy-bottomed skillet (cast iron) over high heat until just smoking. Add 1 tbsp oil. Place steaks in the hot pan and sear undisturbed for 2-4 minutes per side until a deep crust forms.
Step 5: Finish Cooking. Transfer skillet to a preheated oven at 375°F (190°C). Cook for 5-8 minutes for medium-rare (130-135°F) or 8-10 minutes for medium (135-140°F), using a meat thermometer.
Step 6: Rest Steaks. Remove steaks to a cutting board, tent with foil, and rest for 5-10 minutes.
Step 7: Make Béarnaise Reduction. In a small saucepan, combine vinegar, white wine, minced shallots, and 1 tbsp tarragon. Simmer until liquid reduces by two-thirds. Strain and let cool slightly.
Step 8: Whisk Egg Yolks. In a heatproof bowl, whisk egg yolks into the cooled reduction until light and frothy.
Step 9: Create Double Boiler. Place bowl over a saucepan of simmering water (not touching water). Continuously whisk egg mixture until it thickens and coats the back of a spoon.
Step 10: Emulsify Butter. Slowly, in a thin, steady stream, whisk in the warm melted butter until the sauce is thick, smooth, and glossy. Remove from heat.
Step 11: Finish Béarnaise. Stir in remaining chopped tarragon, lemon juice, salt, and white pepper. Keep warm.
Step 12: Warm Crab. Gently warm seasoned crab meat in a microwave for 30 seconds or in a small skillet over low heat.
Step 13: Plate and Serve. Place a steak on each plate. Arrange asparagus spears on or alongside. Spoon warmed crab meat over asparagus/steak. Drizzle generously with béarnaise sauce. Serve immediately.