Preheat your oven to 400°F (200°C).

Rub the beef tenderloin with 2 tablespoons of olive oil, then season generously with kosher salt and black pepper.

In a small bowl, combine the minced garlic, chopped chives, rosemary, thyme, and Dijon mustard. Mix well to form a paste.

Spread the herb mixture evenly over the surface of the tenderloin, pressing it gently to adhere.

In a large oven-safe skillet, heat the remaining 2 tablespoons of olive oil over medium-high heat. Add the tenderloin and sear on all sides until browned, about 3-4 minutes per side.

Transfer the skillet to the preheated oven and roast the tenderloin for 25-30 minutes, or until it reaches your desired doneness (135°F for medium-rare).

While the tenderloin is roasting, melt the butter in a saucepan over medium heat. Add the sliced shallots and cook, stirring frequently, until they are caramelized and golden brown, about 10-12 minutes. Stir in the balsamic vinegar and cook for an additional 2 minutes.

Once the tenderloin is cooked, remove it from the oven and let it rest for 10-15 minutes before slicing.

Slice the tenderloin and drizzle the caramelized shallot butter over the top. Garnish with fresh herbs if desired.