Dredge the beef in the flour and season with salt and pepper to taste. In a skillet set over moderately high heat, heat the oil until it is hot. Add the meat and toss it until it is no longer pink. Transfer to a plate. Add the butter to the pan and heat it until melted. Add the shallot and cook, stirring, 1 minute. Add the mushrooms, garlic and salt and pepper to taste and cook, stirring, for 5 to 7 minutes, or until lightly golden. Add the Madeira and reduce by half. Add the broth and tomato paste and bring back to the boil. Return the meat to the pan and simmer until heated through. Transfer the noodles to a serving plate, top with the beef and garnish with the chives.