Stir butter, salt, mustard, pepper, and garlic.
Place beef on a wire rack in a rimmed baking sheet. Rub butter mixture all over beef, and chill, uncovered, at least 8 hours.
Let beef stand about 20 minutes at room temperature. Returning to room temperature before cooking helps the tenderloin to cook more evenly.
Preheat oven to 425°F.
Bake in preheated oven until meat thermometer inserted into the middle of the tenderloin registers 135°F, which takes 25 to 30 minutes. This is an exact medium-rare.
While cooking, heat the balsamic vinegar in a pan for 15-20 minutes on medium-high heat and let reduce until the reduction thinly coats the back of a spoon. It will change from tasting like vinegar, to tasting sweet and savory.
Cover with aluminum foil; make sure to let rest about 15 minutes before slicing
Serve with common sides – often a form of potato (baked, mashed, au gratin, etc…) and salad