Sprinkle all sides of the 13 to 5-lb beef tenderloin roast with sea salt and place it uncovered in a casserole dish or large Tupperware. Refrigerate up to 12 hours.
Two hours before cooking, remove the tenderloin from the refrigerator and set it on the counter to come to room temperature. Sprinkle the whole roast evenly with Italian Seasoning.
Preheat the oven to 425°F (218°C).
Place a cast-iron or other heavy skillet on the stove and heat it over medium-high until very hot (about 375–390°F if you have an infrared thermometer).
Transfer the beef tenderloin to the hot dry skillet and sear for 3 to 4 minutes per side, turning to brown all sides and the ends, until the exterior develops a golden-brown crust.
Move the skillet with the seared tenderloin into the preheated oven. Roast until an instant-read thermometer inserted into the thickest part reads: 115–120°F for rare (about 10–15 minutes), 120–125°F for medium-rare (about 12–18 minutes), or 130–135°F for medium (about 18–25 minutes). Times are approximate—use the thermometer for accuracy. The internal temperature will rise another 5–10°F while resting.
Remove the tenderloin from the oven and transfer it to a cutting board. Let it rest, uncovered or lightly tented, for 15 minutes.
Cut the strings off the roast, slice the tenderloin into 1/2-inch slices, and serve.