Remove the beef tenderloin from the refrigerator at least 1 hour before cooking and let it rest at room temperature. Pat it completely dry with paper towels on all sides, then season generously all over with kosher salt and cracked black pepper.
Use a sharp knife to remove any remaining silver skin from the surface of the roast. Fold the thinner tail end underneath the roast and tie the entire length with butcher's twine at 1-inch (2.5 cm) intervals to create an even thickness.
In a small bowl, combine the softened butter, minced garlic, chopped rosemary, thyme, parsley, and Dijon mustard (if using). Mix with a fork until fully combined and set aside at room temperature.
Preheat your oven to 425°F (220°C). Place a 12-inch cast iron or heavy oven-safe skillet over medium-high heat for 2–3 minutes until very hot, then add 1 tablespoon of olive oil and swirl to coat.
Place the seasoned tenderloin into the hot skillet and sear on all sides — including both ends — turning every 2–3 minutes until a deep golden-brown crust forms on every surface, about 10–12 minutes total.
Remove the skillet from heat and coat the entire surface of the seared tenderloin with the herb butter rub. Transfer to the preheated oven and roast until the internal temperature reaches 120–125°F (49–52°C) for medium-rare, about 20–30 minutes depending on roast size.
Transfer the roast to a cutting board and loosely tent with aluminum foil. Let it rest for 10–15 minutes — the internal temperature will rise 5–10°F (3–6°C) during this time through carryover cooking.
Place the skillet over medium heat, pour in the red wine, and scrape up all the browned bits from the bottom. Add the beef broth and simmer 5–7 minutes until reduced, then stir in the thyme, season with salt and pepper, and swirl in the cold butter pieces off heat until glossy.
Remove the twine, slice the rested tenderloin into 1–1½ inch (2.5–3.8 cm) rounds using long, smooth strokes. Finish with a sprinkle of flaky sea salt and serve immediately with pan sauce on the side.