Cut the pork tenderloin into 9 or 10 two-inch thick medallions. Sprinkle with salt and pepper.
Heat 1 tablespoon of butter and the olive oil in a large skillet over medium heat. Allow the butter to completely melt and begin bubbling. Add the pork medallions and cook for 5 minutes. Flip them over and cook for 5 more minutes.
Remove the medallions from the pan and place on a plate.
Add the remaining tablespoon of butter to the pan. Once it has melted add the shallots and garlic to the pan. Cook for 3-4 minutes. Add in the mushrooms and cook for 4-5 minutes.
Stir in the flour. Pour in the beef broth and mix well. Boil for 2-3 minutes or until the gravy has thickened. Stir in the milk.
Add the pork medallions and any accumulated juices to the pan. Heat for 2-3 minutes and serve the medallions topped with the mushroom gravy.