Heat a cast iron over high until very hot but not smoking, about 2 minutes. Season the steaks with salt and pepper. Add half butter to the pan and set one of the steaks directly on top .
Repeat with the remaining butter and steak. Do not move them until they are easily released from pan and golden brown crust has formed, about 2 minutes. Using tongs, hold steaks and sear both sides. Then turn steaks over and continue until no red color left and instant read thermometer reaches 125°F for medium-rare, or 140°F for medium. If didn't reach temperature, cover the pan and cook with its own steam
Make sauce: Remove your steaks from pan and the pan from heat. Carefully pour in vermouth (it may spatter). Return skillet to heat. Deglaze pan, stirring up any browned bits with a wooden spoon. Cook until liquid almost completely reduced, about 50 sec. Stir in mustard and heat for 20 seconds.
Add the cream and any juices that have collected from steak and stir to combine. Cook until sauce lightly coats the back of a spoon. About 15 sec. Season with salt and pepper if you need .
Place steaks on dinner plates and pour sauce over, dividing evenly.
