Chop the garlic finely. Sprinkle 1 tablespoon salt over the garlic and continue to chop it, occasionally smashing and smearing the garlic with the flat side of the knife, until the garlic becomes paste-like. (Alternatively, mash the garlic and salt together in a mortar and pestle.) Put the garlic paste, butter, thyme, and pepper in a small bowl. Fold the softened butter over and onto the garlic and thyme, mashing it down with the back of a spoon or spatula. Use a sheet of plastic wrap to help shape the butter into a log, wrap the log well with the plastic wrap, and refrigerate until ready to use. (The garlic butter can be made up to 3 days ahead; it can also be frozen, well wrapped, for a couple of months.)
Melt half of the garlic-butter mixture in a small pan over medium heat. (Rewrap and save the other half for future use; it's great stuff under the skin of a chicken before roasting or tossing into the broth of steamed mussels.)
Heat the oven to 425 degrees F.
In a large ovenproof saute pan, heat the vegetable oil over high heat until very hot. Season the steaks with a little salt and pepper. Add the steaks to the pan and brown them well on 1 side, about 5 minutes. Turn the steaks and brush them liberally with the garlic butter. Finish cooking the steaks in the oven, brushing them occasionally with more garlic butter, until done, about another 5 minutes. (The time will vary depending on how you like your steaks cooked and how thick they are.) Remove the steaks from the oven and allow them to rest for 5 minutes before serving. Serve smaller steaks whole or sliced thinly across the grain. Cut larger steaks into 2 servings or into thin slices. Spoon any remaining juices from the pan onto the meat as well.
Recipe courtesy of Gordon Hamersley, Bistro Cooking at Home, Broadway Books, 2003