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Arrange a rack in center of oven; preheat to 275°. Set a wire rack in a metal baking sheet. Arrange steak on wire rack; season all over with salt and a generous amount of pepper, gently pressing into steak to adhere. (If desired, transfer sheet with rack to the refrigerator and chill 6 to 12 hours.)
Transfer baking sheet to oven and bake until an instant-read thermometer registers 20° below desired temperature (110° for medium-rare, 120° for medium, 125° for medium-well). This should take 25 to 35 minutes for medium-rare (depending on the thickness of the steak) and up to 40 minutes for medium-well.
In a large cast-iron skillet over medium-high heat, heat oil until tiny wisps begin to rise off surface of pan. Using tongs, add steak presentation side down and cook until deeply browned on the bottom, about 1 minute.
Flip steak and add butter. Using a thick kitchen towel or heatproof oven mitt, grasp handle of pan and tilt it down toward you so melting butter begins to pool at the bottom. Add garlic and thyme to area of pan 'above' the steak. Using a large metal spoon, spoon frothing butter over top of garlic, herbs, and steak. Continue to baste until steak is glistening, about 30 seconds.
Transfer steak to a large cutting board. Let rest 5 to 10 minutes, then slice against the grain.