Prepare the steaks. Pat the steaks dry with paper towels. Season both sides generously with salt and pepper. Press the pepper onto the steaks so they stick and let sit on the counter for 1 hour.
Sear the steaks. Heat up the butter and oil in a heavy-bottomed pan or cast-iron skillet over medium-high heat. Once the oil shimmers, add the steaks. Sear for 3–4 minutes per side for medium-rare (adjust time based on thickness). Transfer steaks to a warm plate and loosely cover with foil. Resting the steaks before slicing ensures the juice are evenly distributed.
Make the sauce. Lower heat to medium. In the same pan, sauté the minced garlic and shallot until golden for about 1 minute. Carefully deglaze with cognac, scraping up browned bits. Add the crush peppercorns and beef stock, bring to a simmer and reduce by half. This should take about 4-5 minutes. Add heavy cream and Dijon, stirring constantly until thickened for about 3 minutes.
Don’t overcook the sauce—cream can break if boiled too hard or too long.
Season with salt to taste.
For serving, slice the steaks into strips, place on plates and spoon the warm peppercorn sauce over each one.
Serve immediately with French fries, mashed potatoes, or a simple green salad.