In a small bowl, mix the butter with the mustard. Scrape the compound butter onto a small piece of parchment paper. Roll the parchment paper into a cylinder and shape the butter into a log. Twist the ends to secure and transfer to the refrigerator or freezer until solid.
Season the steaks all over with salt and pepper and drizzle with oil (I find that oiling the steaks produces less smoke in the pan). In a large cast iron skillet, cook the steaks over moderately-high heat until well browned, about 2 minutes. Flip and top each steak with a small knob of the mustard compound butter. Cook until medium-rare within, roughly 2 to 4 minutes more depending on the thickness of your meat. Transfer to a work surface and let rest for 10 minutes.
Slice the steaks against the grain and transfer to plates. Top each steak with a knob of the mustard compound butter and sprinkle with flaky sea salt. Serve right away with a simple green salad and French fries.