Heat a 10-in. nonstick omelette or fry pan on medium-high heat. Add the oil to the pan and heat through. Season the beef tenderloin steaks with salt and pepper.
Place the seasoned steaks into the hot pan. Allow the steaks to sear for 5 minutes before turning to cook the second side. Cook the second side for 4 minutes. Check the flame. If it is too high and it seems that the steaks are burning, reduce the heat. Remove the steaks from the pan.
Add the shallots, garlic, thyme and mushrooms to the pan. Sauté for 1 minute.
Deglaze the pan with brandy. Be careful, as the liquor might ignite. Reduce the brandy by half.
Add the green peppercorns, demi glace and cream. Combine well and reduce until a slightly thickened.
Adjust the seasoning of the sauce with salt and pepper. Mix in the parsley. Pour the sauce over the steaks and serve.