Remove steak from the refrigerator 40-60 minutes before cooking. Pat the surface dry with a paper towel. Season both sides with salt and pepper. Let stand at room temperature until ready to cook.
Heat a large cast iron skillet over high heat until very hot. (Test the temperature by adding a few droplets of water to the pan. They should evaporate immediately.) Add the vegetable oil to the pan and continue to heat until it shimmers and just a few light wisps of smoke rise from the edges.
Pat the steak dry again and add it to the pan with tongs. Let it cook for 2 minutes, then flip it to the other side to cook for 2 minutes longer.
Flip the steak again and add 2 tablespoons butter to the sides of the pan, letting it melt until foaming. Start to baste the top of the steak with the hot butter, gently tilting the pan if needed to collect it with your spoon. Continue cooking and basting for about a minute before flipping the steak again.
Add the remaining 1 tablespoon of butter, garlic cloves, and herbs to the pan. Continue basting the steak with the infused, browned butter, flipping once or twice more, until the steak is golden on both sides and registers 110-115 degrees F for rare, 120-125 for medium rare, or 128-130 for medium.*
Transfer the steak to a cutting board and tent with foil. Rest for 10 minutes before slicing and serving, drizzling with any accumulated juices and a little browned butter. Sprinkle the sliced meat with a pinch of coarse sea salt, if desired.
*Keep an eye on the butter and garlic. If they're getting too brown, reduce the heat.