Take steaks out of the fridge and let them come to room temperature for about 30 minutes.
Pat steaks dry with paper towels. Season both sides generously with salt and pepper.
Heat a cast iron skillet over medium-high heat for 4–5 minutes until very hot.
Add 1 tablespoon of neutral oil to the pan. Place steaks in the pan and don’t move them for 2–3 minutes to get a good sear.
Flip steaks and sear the other side for another 2–3 minutes. If steaks are thicker than 1 inch, sear the edges briefly too.
Reduce heat to medium. Add 1 tablespoon of butter and spoon melted butter over steaks for 1 minute.
Use an instant-read thermometer to check internal temperature: 130–135°F for medium-rare. Remove steaks 3–5°F before target temperature.
Transfer steaks to a plate and loosely tent with foil. Rest for 5–7 minutes.
While steaks rest, add chopped shallots to the pan and sauté for 30–60 seconds.
Pour in beef broth and scrape up browned bits from the pan.
Stir in Dijon mustard and optional splash of wine or vinegar.
Turn off heat and whisk in 1 tablespoon cold butter until sauce is glossy.
Serve steaks sliced against the grain with pan sauce poured on top or on the side.