In a large skillet, melt butter with olive oil. Season meat with salt and pepper to taste and cook over high heat until lightly browned on the bottom, about 1 minute. Turn medallions and cook for 45 seconds longer, then transfer to a plate and tent with foil.
Add shallot and garlic to skillet and cook over moderate heat, stirring, until fragrant, about 20 seconds. Add mushrooms, season with salt and pepper to taste, and cook until softened, about 2 minutes.
Remove pan from heat, add Cognac, and carefully ignite it with a long match.
When flames die down, add mustard and cream and stir over moderate heat for 1 minute.
Whisk in the veal demiglace, Worcestershire sauce, scallions, and parsley; season with salt, pepper, and hot sauce to taste.
Add meat and any accumulated juices to saucepan and turn to coat. Simmer until heated through, about 1 minute. Transfer meat to plates, spoon sauce on top, and serve.