Heat oven to 200ºF.
Sprinkle steaks with kosher salt and crushed black pepper. Heat butter in a 12-inch, heavy-bottomed saute pan over medium heat. Once butter is hot, add steaks and cook until browned on both sides, 2 minutes per side for medium-rare and 3 minutes per side for medium. Remove steaks from pan and place on a rack set on a half-sheet pan; place in oven to keep warm.
Add the stock to the saute pan and whisk until the crispy bits release from bottom of pan. Allow the liquid to reduce for 3 to 4 minutes over medium-high heat. Add the cognac, heavy cream, and green peppercorns to the pan. Increase heat to high and cook, whisking continuously, until sauce thickens slightly, just enough to coat the back of a spoon, 5 to 7 minutes.
Season the sauce to taste with kosher salt. Place steaks on plates, top with sauce, and serve immediately.