Remove steak from fridge for 20 to 30 minutes to bring it to room temperature. Pat steak dry with a paper towel and season generously with salt and freshly ground black pepper on both sides.
Heat butter in a large skillet over medium-high heat. When butter melts, add steak and garlic, cut side down. Sear until the underside of the steak is nicely browned, about 8 minutes.
Flip steak and rub the cut side of garlic over the steak. Leave garlic in the pan to cook with the steak.
Add rosemary sprigs to the pan and continue cooking for 5 minutes. Reduce heat to low and cook for another 3 minutes.
Remove steak from pan and let it rest for 5 minutes before serving.