Add olive oil to a large heavy skillet (preferably cast iron) and place over MEDIUM-HIGH heat. Cook pork medallions for about 3 minutes per side, until nicely browned and cooked through. Remove to a plate and set aside.

Reduce heat under skillet to MEDIUM and add butter. When butter has melted add onion and garlic and cook, stirring. When onions have slightly softened, add mushrooms and fresh thyme. Cook and stir for several minutes until mushrooms are tender. Add red wine to skillet and cook for a minute or two and then add beef broth, Worcestershire sauce, and Dijon mustard. Increase heat under skillet as needed to bring mixture to a low boil and simmer for a minute or two. Reduce heat to LOW.

Meanwhile, combine heavy cream (or half and half) with cornstarch in a small bowl, mixing until well combined. Add to skillet and stir until sauce has thickened slightly. Season with salt and pepper, to taste.

Nestle the cooked pork medallions into the sauce and serve.