Remove the beef tenderloin from the refrigerator 1 hour before cooking to bring it to room temperature. Pat the entire surface completely dry with paper towels.
If your butcher hasn't already done so, trim any excess fat or silver skin from the surface. Tie the tenderloin with kitchen twine at 2-inch intervals to create an even thickness.
In a small bowl, combine the softened butter, Dijon mustard, minced garlic, chopped rosemary, thyme, salt, and black pepper. Mix everything together with a fork until you have a thick paste.
Brush the entire surface of the beef with olive oil, making sure to coat all sides evenly. Spread the herb mixture all over the tenderloin, pressing it gently so it adheres to the meat.
Let the seasoned beef sit at room temperature for 30 minutes while you preheat the oven to 425°F (220°C).
Heat the cast iron skillet over high heat until it's smoking hot, about 3-4 minutes. Carefully place the tenderloin in the hot skillet and sear for 2-3 minutes per side, turning with tongs to brown all sides.
Transfer the seared tenderloin to a roasting pan fitted with a rack. Place the pan in the preheated oven on the center rack.
Roast for 35-45 minutes, depending on your desired doneness and the thickness of your roast. Start checking the internal temperature after 30 minutes using your meat thermometer.
For rare, aim for an internal temperature of 120°F (49°C). For medium-rare, aim for 130°F (54°C). For medium, aim for 140°F (60°C). Remove from the oven slightly before it reaches your target temperature.
Transfer the tenderloin to a cutting board and tent it loosely with aluminum foil. Let it rest for at least 15-20 minutes to allow the juices to redistribute throughout the meat.
Remove the kitchen twine carefully with scissors or a sharp knife. Using a sharp carving knife, slice the tenderloin into 1-inch thick medallions.
Arrange the slices on a serving platter and spoon any accumulated juices over the top.