Begin by patting the steak medallions dry with a paper towel. Season both sides generously with salt and freshly ground pepper.
Heat the olive oil in a large skillet over high heat. Place the seasoned steaks in a single layer within the pan. To avoid overcrowding, cook in batches if necessary.
Sear the steak medallions for 3–4 minutes on each side, or until they reach your preferred level of doneness. For precise results, use a meat thermometer to check the internal temperature.
Once cooked, remove the steaks from the pan and transfer them to a plate. Cover them loosely with foil to retain warmth.
Lower the heat to medium and melt the butter in the same skillet. Add the mushrooms and sauté for 4–5 minutes, stirring intermittently, until they become golden brown and tender.
Stir in the minced shallots and garlic, cooking for an additional minute. Adjust seasoning with salt and pepper as needed.
Carefully pour the cognac into the skillet, allowing it to deglaze the pan. Bring the mixture to a boil and cook for 1–2 minutes, letting the liquid reduce by half.
Introduce the beef broth, Dijon mustard, Worcestershire sauce, and heavy cream to the pan. Whisk the ingredients thoroughly until a smooth sauce forms.
Reduce the heat to a gentle simmer and let the sauce thicken over 3–4 minutes, stirring occasionally to prevent sticking.
Return the steak medallions to the skillet, spooning the sauce over each piece to coat them evenly.
Garnish with freshly sliced chives and serve immediately.
