For the surf:
In a medium bowl, stir the crabmeat together with the mayonnaise, chili paste, cilantro, and lime juice, and season with salt and pepper. Cover with plastic wrap and set aside in the refrigerator.
For the turf: Preheat the oven to 400 degrees F.
Put a cast iron or ovenproof skillet over medium-high heat and get it hot. Drizzle in a 2-count of oil. If you choose to tie the fillets, take a piece of butchers twine and wrap it around each fillet twice to form a nice round shape. This will help the meat retain its shape while cooking. Sprinkle the beef all over with salt and pepper and sear for about 3 minutes on each side, until well browned. Shove the beef to the side and add the tomatoes to the pan; drizzle with olive oil, sprinkle with salt and pepper, and stir gently to coat. Now put the pan in the oven and roast until the beef is rare and the tomatoes burst, 7 to 8 minutes. (Add 2 more minutes for medium rare, 5 more minutes for medium.)
For service: Wash the arugula and toss it in a bowl with olive oil and lemon juice. Season with a few turns of freshly ground black pepper.
To serve, arrange the steaks on a serving plate. Spoon the crab salad over the meat and scatter the tomatoes on top. Drizzle with olive oil. Serve with a small tangle of dressed arugula and a glass of rose wine.