Put an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Spray a heavy baking sheet with vegetable oil cooking spray. Set aside.
In a large skillet, heat the oil over high heat. Season the beef with salt and pepper and brown on all sides, for about 5 minutes. Transfer the beef to the prepared baking sheet and roast until an instant-read thermometer inserted into the thickest part of the meat registers 125 degrees F for medium-rare, about 40 to 45 minutes. Remove the beef from the oven to a cutting board. Cover the meat loosely with foil and let rest for 20 minutes.
Sauce: In a blender, combine the pineapple chunks and syrup, the orange juice, lemon juice, soy sauce, sugar, arrowroot, garlic, ginger, and 1/2 teaspoon salt. Blend until smooth. Heat the same skillet used for the beef over medium-high heat. Add the sauce and scrape up the brown bits that cling to the bottom of the pan with a wooden spoon. Simmer until the sauce thickens, about 5 minutes Season with salt, to taste.
Cutting across the grain, slice the meat into 1/4-inch thick slices and arrange on a platter. Garnish with orange slices, if using. Pour the sauce into a serving bowl and serve alongside the beef.
Garnish: orange slices, optional.
Recipe courtesy of Giada De Laurentiis