Peel the garlic cloves and smash them with the side of a knife. Mince and sprinkle lightly with salt.
Pat the steak dry and season with salt and pepper. Place the oil in a heavy pan and heat it over medium-high heat. Add the steak and let cook 2-3 minutes per side for medium rare. Transfer the steak to a plate and let rest.
In a small skillet, melt the butter over low heat. Add the garlic and thyme leaves, and let cook until butter turns golden brown. About 4 minutes. Lightly salt to taste.
Slice the steak, and spoon the garlic-thyme butter over the steak.