Preheat your oven to 350°F (175°C). Season the beef tenderloin pieces on both sides with salt and ground pepper. Let the meat rest at room temperature for a few minutes.
In a large skillet, melt 1 tablespoon of butter over medium heat. If needed, add 1 tablespoon of vegetable oil to prevent the butter from burning. Place the seasoned steaks in the skillet and sear them for 1 to 2 minutes on each side until they develop a nice brown crust.
Transfer the seared steaks to a roasting pan or tray and place them in the preheated oven. Roast the steak for at least 5 minutes, or until it reaches your desired level of doneness. Keep in mind that the meat will continue to cook even after being removed from the oven, so slightly undercook it if you prefer medium-rare. Once done, cover the steaks with foil to retain heat while you prepare the sauce.
Using the same skillet, add the remaining tablespoon of butter. Toss in the chopped onions and sliced mushrooms, sautéing them for 1 to 2 minutes until they begin to soften.
Next, carefully deglaze the skillet by adding the cognac or brandy. Let the alcohol cook off and the liquid reduce slightly. Stir in the Worcestershire sauce, mustard, and beef stock. Allow the sauce to simmer for about 10 minutes, or until it has reduced by half. To finish, gradually whisk in the cream, thickening the sauce. Season to taste with additional salt and pepper, if needed.
Place the roasted steaks on plates, generously spoon the Diane sauce over the top, and serve immediately. Accompany the steak with a baked potato and a side of roasted vegetables for a complete, hearty meal.