For the steaks: In a baking dish, sprinkle the steaks on both sides with the salt and pepper and drizzle with the oil. Place the rosemary in the dish and allow to marinate on the counter at room temperature for 1 hour, turning the steaks halfway through to infuse all over with rosemary.
For the rosemary butter: In a saucepan over medium-low heat, add the butter and salt. Stir to melt the butter and dissolve the salt, then add the rosemary. Continue cooking on low until the butter is fragrant from the rosemary, 10 to 12 minutes. Remove the rosemary and discard.
Preheat a grill or grill pan to high heat. Remove the steaks from the baking dish, discard the rosemary and place the steaks directly on the grill. Cook for about 5 minutes on both sides for medium-rare. Remove from the grill and allow to rest under loosely fitted aluminum foil for 10 minutes.
Using the direction of the muscles as a guide, thinly slice the meat against the grain into strips and place on a serving dish. Pour the infused butter over the meat and serve.