Pre-heat your oven to 275 degrees. Make sure that your oven temperature is accurate!
Place your tenderloin on sheet pan (I like to line mine with aluminum foil for easy cleanup) and pat the whole thing dry using paper towels. Brush the beef on all sides with 2½ tablespoons of the olive oil. No brush? No problem. Just use your hands to rub the oil over the meat. Season the beef with the salt and pepper, making sure the entire tenderloin is given some love. (It may seem like a lot of salt, but trust me, it will make your meat perfectly delectable.)
Secure the rosemary sprigs to your tenderloin by threading them through the kitchen string tying the beef at 2-inch intervals. Brush the rosemary sprigs with the remaining ½ tablespoon of olive oil.
Transfer your tenderloin to the oven and cook for 1 hour to 1½ hours until the internal temperature in the center of the meat is 125 degrees for rare or 135 degrees for medium rare. The best way to get an accurate reading is to stick the thermometer horizontally through the end of the beef. (I know a half hour is a large window of cooking time, but it will vary slightly based on the weight of your tenderloin. I strongly recommend checking the internal temperature of your beef after 1 hour to assess the situation.)
Cover your cooked tenderloin with aluminum foil and let it rest for at least 20 minutes.
Slice your beef thickly and serve warm or at room temperature.