Preparation

• Season the tenderloin all over with 3/4 tsp. salt and 1/2 tsp. pepper. Put the tenderloin on a flat rack in a roasting pan, and refrigerate for at least 1 hour and up to 1 day. Let the tenderloin come to room temperature for 1 hour before roasting.
• Position a rack in the center of the oven, and heat the oven to 300°F. Roast the beef until an instant-read thermometer registers 115°F for rare or 120°F for medium rare, about 45 minutes. Remove the roast from the oven. Let sit, loosely tented with foil, for up to 2 hours.
• Prepare a high (500°F to 600°F) gas or charcoal grill fire. Clean and then lightly oil the grill grate. Put the roast on the grill, and sear on all sides until evenly browned, rotating often and moving it away from flare-ups as necessary, 1 to 2 minutes per side. Transfer to a cutting board, and set aside.
• Put the arugula in a medium bowl. Toss with 1 Tbs. of the olive oil, the vinegar, ¼ tsp. salt, and 1/8 tsp. pepper, and transfer to a large serving platter. Trim the ends of the tenderloin, and cut the beef into twelve 3/4-inch-thick slices.
• Arrange alternating slices of tomato, mozzarella, and beef on the arugula with a basil leaf tucked between each slice. Drizzle with the remaining 3 Tbs. olive oil. Sprinkle with 1/2 tsp. salt and several grinds of pepper, and serve.