First, take your steaks out of the refrigerator about an hour before you plan to cook. Pat them completely dry with paper towels and season them generously on all sides with kosher salt. Place your whole peppercorns on a cutting board and use the flat side of a meat mallet or a rolling pin to crush them into coarse pieces. Press both sides of each steak firmly into the crushed peppercorns to create an even crust.
Heat your large pan over medium heat and add the neutral oil. Once the oil shimmers, carefully place the steaks in the pan. Let them cook undisturbed for about 4 minutes on the first side to develop a beautiful crust. Flip the steaks and cook for another 4 minutes for a medium-rare finish. If your steaks have a thick fat cap on the side, use tongs to hold them upright and sear that edge until browned.
Once cooked to your liking (125°F on an instant-read thermometer for medium-rare), transfer the steaks to a cutting board. Tent them loosely with foil and let them rest. This crucial step allows the juices to redistribute throughout the meat, ensuring a tender and flavorful steak.
Pour off any excess fat from the pan, leaving the browned bits. Add the minced shallot and a pinch of salt, and sauté for 2-3 minutes until softened. Carefully remove the pan from the heat, pour in the cognac, then return it to the stove. Let the cognac bubble and reduce by about half, scraping the bottom of the pan with a wooden spoon to lift all the flavorful fond.
Pour the heavy cream into the pan and bring it to a simmer. Cook for 2-3 minutes, allowing the sauce to thicken until it can coat the back of a spoon. If using, stir in the green peppercorns. Turn off the heat and whisk in the cold butter until it's fully melted and the sauce is glossy. To serve, spoon some of the sauce onto each plate, place a steak on top, and pour the remaining sauce over it.