Preheat your oven to 450ºF. In a small food processor, combine the garlic and salt, and process until the garlic is finely chopped.
Add the 1/3 cup olive oil, black pepper, and thyme, and process until the herbs are evenly chopped.
Stir in the mustard and vinegar.
Heat a large cast-iron skillet or Dutch oven on the stovetop.
Add the remaining 2 tablespoons of olive oil and heat until it shimmers.
Sear the beef tenderloin on all sides until nicely browned, 3 to 4 minutes per side, turning with tongs.
Transfer the meat to a cutting board and let cool slightly.
Coat the meat evenly on all sides with the garlic mixture.
Transfer it to a meat rack set in a roasting pan.
Roast the tenderloin until the internal temperature reaches your desired doneness on an instant-read thermometer, about 20 to 30 minutes (depending on its thickness).
Let it rest for at least 10 minutes before slicing and serving.