1.Preheat the oven to 450 degrees F.
2.In the meantime start the balsamic vinegar reduction.
3.In a medium saucepan, combine the vinegar, carrots, celery, onion, bay leaves, and rosemary needles.
4.Bring to a boil, and simmer until the vinegar has reduced by half, about 30 minutes.
5.Strain the vinegar into a clean saucepan, and keep warm.
6.Discard the vegetables and herbs.
7.Season the beef with salt, and coat with the olive oil. Heat a -cast–iron skillet over high heat. When the skillet is hot, sear the beef on all sides, then set the skillet in the preheated oven to roast until -medium-rare, about 15 minutes. Let rest on a cutting board for 10 minutes, then slice.
To serve: Once the filet is sliced, sprinkle with coarse salt and drizzle with olive oil, then with a spoon lightly drizzle the filet slices with the balsamic-vinegar reduction.