Season the steaks generously with salt and pepper. Heat a large, heavy skillet (such as cast iron) over medium-high heat and add the oil. When the oil is hot, add the steaks, and sear for about 4 minutes on each side, until nicely browned on the outside and cooked to your liking, about 125°F internal temperature for rare, 135°F for medium-rare. Transfer them to a cutting board, and tent them with foil. Pour off any remaining fat from the skillet, but do not clean the skillet.
Melt the butter in the same skillet over medium-low heat. Sauté the shallots for 4 minutes, until golden brown and tender. Add the mustard, Worcestershire sauce, red wine and cognac (be careful, the liquor can ignite) and stir, scraping up any little browned bits from the bottom of the pan. Allow the sauce to reduce a bit, just one minute, then taste and season as needed. Stir in the parsley.
Slice the steaks and transfer them to a serving plate, or serve each steak on an individual plate with the desired side dishes. Drizzle the sauce over the steak and serve.
Notes
What is Steak Diane?
The origin of the name is unclear (other than possibly being linked to Diane, the Roman Goddess of the Hunt). Traditionally the cut of beef used for Steak Diane is very thin (often pounded to be so). I wanted to see how to pull these flavors onto a big fat juicy steak, so I picked a couple of nice 1-inch thick strip steaks as my canvas.