Thirty minutes prior to cooking, place beef tenderloin on a platter, season with salt, pepper, and thyme, and rub generously with olive oil. Cover and bring to room temperature.

Place a cast iron pan large enough to hold tenderloins over high heat; when hot, coat the bottom of the pan with olive oil. Sear tenderloin one side until browned, about 4 minutes. Turn and sear for 4 more minutes for rare. (If you prefer steaks less rare, place pan in preheated 425°F oven and cook to desired internal temperature, 135°F for medium rare, 145°F for medium, 155°F for medium well, over 160°F for well done.)

Remove tenderloins to a clean platter and allow to rest for ten minutes. In the same skillet, melt butter over medium heat. Add the jumbo lump crab meat and parsley and stir gently to combine. Heat through.

Top each steak with crabmeat mixture and pass the Bernaise Sauce at the table.