Set an oven rack in the middle position and preheat the oven to 400 degrees Fahrenheit.
Heat the oil in a large oven-proof skillet over medium-high heat (a cast iron skillet works well). When the oil is hot, place the roast in the skillet and sear the meat on all but one side until golden brown. With kitchen tongs, turn the meat so that the un-seared side is down.
Transfer the skillet to the pre-heated oven and roast for about 15 minutes, depending on the size of your roast, until an oven-safe meat thermometer inserted into the thickest part of the tenderloin registers 120 degrees Fahrenheit for medium rare, or until your desired doneness is reached. The temperature of the meat will continue to rise about 5 degrees after it is removed from the oven while it is resting, before slicing.
Transfer the beef roast to a cutting board or platter and allow it to rest, covered loosely with aluminum foil, for about 10 minutes.
Meanwhile, carefully discard some of the fat from the skillet. Set the pan on the stovetop and add the 1/4 cup of beef broth. Bring to a boil and using a wooden spoon scrape the brown bits from the bottom of the pan.
Remove the skillet from the heat and add the broth from the skillet to the red wine sauce. Mix to combine and then bring the sauce to a simmer over low heat for about 2-3 minutes. Remove from the heat.
Slice the beef tenderloin and serve with the wine sauce.