Set a wire rack in a rimmed baking sheet. In a small bowl, stir together 1 tablespoon each salt and pepper, the nutmeg and sugar. Measure out and reserve 2 teaspoons of the seasoning mixture, then rub the remainder onto all sides of the steaks, pressing it into the meat. Place the steaks on the rack and refrigerate uncovered for at least 1 hour or up to 24 hours.
Heat the oven to 250°F with a rack in the middle position. Place the baking sheet with the steaks in the oven and cook until the centers reach 95°F, 15 to 30 minutes, depending on thickness. Remove from the oven and let stand for at 1 hour.
In a 10- or 12-inch cast-iron skillet over medium-high, heat the oil until barely smoking. Place the steaks in the skillet and cook, without moving them, until well browned, about 3 minutes. Using tongs, flip the steaks and cook until the second sides are well browned and the centers reach 120°F (for medium-rare), 2 to 3 minutes. Alternatively, the steaks can be seared for the same time over direct heat on a very hot charcoal or gas grill with a well-oiled grate.
Transfer the steaks to a carving board and let rest for 10 minutes, then cut into thin slices. Place on a platter, pour on the accumulated juices and sprinkle with the reserved seasoning mixture. Drizzle with a few spoonfuls of chimichurri and serve with additional chimichurri on the side.