Preheat the oven to 400 degrees F.
Tie the tenderloin with kitchen twine in 3 or 4 places around the circumference to help it hold its shape. Put a medium cast iron or ovenproof skillet over medium-high heat and get it hot. Drizzle in a 2-count of oil. Sprinkle the tenderloin all over with salt and pepper and sear it in the hot pan, turning, until well browned. Then put the pan in the oven and roast until the internal temperature of the beef reaches 125 degrees F on an instant-read thermometer, about 20 minutes. Remove the beef to a platter and let it rest 10 minutes.
Turn the oven to broil. Toss the tomatoes on a sheet pan with salt, pepper, and a drizzle of oil. Put the pan under the broiler and broil until the tomatoes burst, about 5 minutes. Dump them into a bowl and season them again with a drizzle of oil, salt, and pepper. Add the arugula and toss.
To serve, remove the strings from the tenderloin and cut it into slices. Arrange the slices on a serving plate, shingling them. Spoon the crab salad over the meat and scatter the tomatoes and arugula over the top. Serve hot.
Stir the crabmeat with the mayonnaise, chili paste, cilantro, and lime juice in a bowl, and season with salt and pepper.
Yield: 4 servings