Rub the tenderloin with three-quarters of the salt, wrap it tightly in plastic, and refrigerate for at least 4 hours and up to 2 days.
Preheat the oven to 225°F (105°C). Line a rimmed baking sheet with aluminum foil, turning up the foil’s edges.
Remove the tenderloin from the refrigerator, pat it dry with paper towels, then place it on the foil-lined pan. Rub the meat with the oil, season with the remaining salt and the pepper, then cook until a meat thermometer inserted into the center reads 120°F to 125°F, 1-1/2 to 2-1/2 hours, depending on your oven and the meat’s temperature after coming out of the refrigerator.
Meanwhile, in a small sauté pan, combine the butter, garlic powder, thyme, and rosemary. Heat over medium heat until the butter melts and begins to bubble. Keep warm. Place an oven rack 6 inches from the broiler. Preheat the broiler.
Pour the melted-butter mixture over the roast. Return roast to the oven and broil about 4 inches from the heat source for 2 minutes to quickly develop a crust.
Remove the roast from the oven, let it rest for 15 minutes, slice, drizzle with butter sauce/pan drippings, sprinkle with salt, and serve.