Season steak generously with kosher salt and pepper and let sit at room temperature 1 hour.
Heat a dry large skillet, preferably cast iron, over medium-high, then add oil. After oil is heated add steak, turning every 1-2 minutes, until outer layer browns and the internal temperature should reach 120°F–125°F for medium-rare, (8–10 minutes).
Add butter, rosemary, and garlic to skillet, tilt pan toward you so that butter pools on one side and use a large spoon to continually baste steak with butter. Continue until butter is no longer bubbling and it smells nutty and is beginning to brown, about 1 minute. Transfer meat to a cutting board and let rest 10 minutes. (For medium-rare, your steak should reach an internal temperature of 125°F–130°F.)
Cut meat, slice against the grain 1" thick. Spoon some infused brown butter over steak and sprinkle with sea salt.