Trim excess fat and remove the silver skin from the beef tenderloin. Cut into 1-inch thick medallions and season with salt and pepper.
In a skillet over medium-high heat, add olive oil and one tablespoon of butter. Sear beef medallions for about three minutes on each side until browned.
Transfer beef to a plate. In the same skillet, add two tablespoons of butter and sliced mushrooms. Cook for 5-6 minutes until golden brown.
Stir in minced garlic, Dijon mustard, Italian seasoning, and broth or vinegar. Allow to bubble for about a minute.
Pour in the heavy cream and let it bubble gently for another minute while stirring continuously.
Add seared beef back into the pan and cook for an additional 3-5 minutes until heated through and coated in sauce.
Taste and adjust seasoning with salt and pepper before serving immediately over rice, pasta, or alongside roasted vegetables.