Allow chateaubriand to come up to room temperature for about an hour. Start your oven or grill, preheating to 225 °F.
While you preheat the oven or grill, oil and season the meat with a thin, even coat of olive oil over the entire chateaubriand, and a generous amount of sea salt. Pepper is optional.
In a medium sized mixing bowl, toss potatoes in 2 tablespoons of olive oil, 2 teaspoons of sea salt and rosemary. Pour into a large cast iron pan, adding the cubed butter.
Place meat on top of potatoes and insert a reliable leave-in meat thermometer into the thickest portion of the meat.
Place pan in preheated oven or grill, and close lid. Allow meat to reach an internal temperature of 120 °F.
Remove the pan from the grill. Then, remove the meat from pan and set aside, leaving potatoes in the pan. Cover the potatoes with aluminum foil. Increase the grill or oven temperature to 550 °F.
If you're using a grill, place meat directly over heat and sear on all sides for about 2 minutes on each side, turning constantly. If you're using an oven, place the meat back in the oven for two minutes, then flip and cook an additional two minutes before removing it from the oven and placing it back on the potatoes. Cover with foil and let it rest.
Slice meat, spoon drippings over top of potatoes, and garnish with fresh parsley before serving.