Tip:Tip: It’s important to let the beef rest before slicing it; this allows the juices to redistribute from the outside of the roast throughout the whole roast, making this lean cut very juicy.
Position a rack in the center of the oven and heat the oven to 450°F. Brush or rub the beef with the oil and put the beef in a 9x13-inch roasting pan lined with aluminum foil. Season the beef generously with salt and pepper.
Roast the beef until an instant-read thermometer registers 120°F to 125°F for rare, about 25 min.; 125°F to 130°F for medium rare, about 30 min. (The temperature of the beef will rise 5°F as it rests.) Wrap the beef in the foil that lines the pan and let rest on a carving board for 10 to 15 min.
While the beef roasts, make the sauce. Melt 2 Tbs. of the butter in a 12-inch skillet over medium heat. Add the shallots and cook, stirring often, until they soften and turn golden brown, 8 to 10 min. Add the wine and the rosemary sprig and bring to a boil over medium-high heat. Boil until the volume of wine and shallots reduces to 1/2 cup, about 3 min. Add the broth and continue to boil until the sauce is reduced to 1 cup, about 5 min. Reduce the heat to low. Remove the rosemary sprig and stir in the chopped rosemary. Cut the remaining 2 Tbs. cold butter into small cubes and add a few of them at a time to the sauce, stirring to melt each addition.
Unwrap the tenderloin and stir any accumulated juices into the sauce. Season the sauce to taste with salt and pepper. Slice the meat and serve with the sauce.