Pat the steaks completely dry with a paper towel. Season generously on both sides with coarse salt and black pepper.
Heat a large cast iron skillet over medium high heat until it is smoking hot.
Add the vegetable oil to the pan, swirling to coat the bottom.
Carefully place the steaks in the skillet. Cook without moving them for 3 to 4 minutes to develop a dark crust.
Flip the steaks. Immediately add the butter, smashed garlic, and rosemary sprigs to the pan.
As the butter melts, tilt the pan slightly toward you. Use a spoon to continuously scoop the foaming butter and pour it over the steaks for about 2 minutes.
Use a meat thermometer to check for your preferred doneness (130 degrees Fahrenheit for medium rare).
Remove the steaks from the pan and transfer to a cutting board. Pour the remaining pan juices and garlic over the top.
Let the steaks rest for 5 to 10 minutes before slicing and serving.