Place cubed potatoes in a pot of cold salted water, bring to a boil, and simmer for 15 to 20 minutes until fork-tender.
Drain potatoes and pass through a ricer or mash thoroughly; incorporate 4 tablespoons of butter and warm milk until smooth. Season with salt and keep warm.
Season steaks with salt on both sides, then press the crushed peppercorns onto the surface of the meat until evenly coated.
Heat vegetable oil and 1 tablespoon of butter in a heavy-bottomed skillet over medium-high heat until the fat is shimmering.
Place steaks in the pan and sear for 4 to 5 minutes per side for medium-rare; remove steaks from pan and tent with foil to rest for 5 minutes.
Discard excess fat from the pan, add cognac carefully (away from open flame), and return to heat to deglaze, scraping up browned bits.
Add beef stock and heavy cream; simmer over medium heat for 3 to 5 minutes until the sauce reduces and thickens to a coating consistency.
Plate the steaks alongside the mashed potatoes and generously spoon the peppercorn sauce over the meat.